Information bit distribution design for polar codes

ABSTRACT

A wireless device (e.g., a base station or user equipment (UE)) may encode a codeword using a polar code for transmission over a wireless channel. The device may identify a set of bit locations of the polar code for a set of information bits based on a bit index reliability sequence. The bit index reliability sequence may be based on applying an ordered combination of a universal partial order, an analytical method, and a simulation. The bit index reliability sequence may be determined based on a binary bit weighting for the set of bit channels that applies one or more weighting factors. In some cases, the device may store the bit index reliability sequence in a lookup table for encoding, decoding, or both. A device receiving the transmitted codeword may similarly utilize the bit index reliability sequence to decode the codeword and determine the transmitted information bits.

CROSS REFERENCES

The present application for patent claims the benefit of U.S.Provisional Patent Application No. 62/540,491 by Jiang, et al., entitled“Polar Sequence Design by Reliability Coefficients Optimization andInformation Bit Distribution Optimization,” filed Aug. 2, 2017 and toU.S. Provisional Patent Application No. 62/544,898 by Jiang, et al.,entitled “Information Bit Distribution Optimization for Polar Codes,”filed Aug. 13, 2017, assigned to the assignee hereof, and expresslyincorporated herein.

BACKGROUND

The following relates generally to wireless communication, and morespecifically to polar sequence design based on coefficient reliabilityand improved information bit distribution.

Wireless communications systems are widely deployed to provide varioustypes of communication content such as voice, video, packet data,messaging, broadcast, and so on. These systems may be capable ofsupporting communication with multiple users by sharing the availablesystem resources (e.g., time, frequency, and power). Examples of suchmultiple-access systems include fourth generation (4G) systems such as aLong Term Evolution (LTE) systems or LTE-Advanced (LTE-A) systems, andfifth generation (5G) systems which may be referred to as New Radio (NR)systems. These systems may employ technologies such as code divisionmultiple access (CDMA), time division multiple access (TDMA), frequencydivision multiple access (FDMA), orthogonal frequency division multipleaccess (OFDMA), or discrete Fourier transform-spread-OFDM (DFT-S-OFDM).A wireless multiple-access communications system may include a number ofbase stations or network access nodes, each simultaneously supportingcommunication for multiple communication devices, which may be otherwiseknown as user equipment (UE).

Wireless communications, however, often involves sending data over anoisy communication channel. To combat noise, a transmitter may encodedata in the form of code blocks using error correcting codes tointroduce redundancy in the code block so that transmission errors maybe detected and/or corrected. Some examples of encoding algorithms witherror correcting codes include convolutional codes (CCs), low-densityparity-check (LDPC) codes, and polar codes. A polar code is an exampleof a linear block error correcting code and is constructed using channelpolarization techniques. Channel polarization takes independent copiesof a transmission channel and transforms the copies into a set ofreliable channels and a set of unreliable channels. Information bits aretransmitted in the reliable channels and bits known a priori by thetransmitter and receiver are transmitted in the unreliable channels. Apolar code has been shown to approach the theoretical channel capacityas the code length approaches infinity. Conventional techniques forselecting reliable channels are deficient.

SUMMARY

The described techniques relate to improved methods, systems, devices,apparatuses, or products by processes that support polar sequence designbased on coefficient reliability and improved information bitdistribution. Generally, the described techniques provide improvedtechniques for identifying a reliability order for channels of a polarcode and information bit distribution design. A transmitter, such as abase station, may determine a bit index reliability sequence for a setof bit channels of a polar code based on a length of the codeword. Someexamples described herein determine a reliability order based on hybridpolarization weighting factors. The hybrid polarization weightingfactors may be applied using nested sequence generation. Additionally oralternatively, hybrid bit index weighting factors may be applied for apolarization weight function. Additional examples described hereincalculate a partial order under a Universal Partial Order (UPO) of aninput search sequence for determining a reliability sequence of channelsof a polar code.

An order of bit indices in the bit index reliability sequence may bedetermined based on applying a UPO to an input search sequence to obtaina partial order, applying an analytical method to obtain calculatedrelative orders of bit indices not ordered in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated relative orders. The transmitter maygenerate the codeword according to the polar code based on the bit indexreliability sequence and a set of information bits encoded using thepolar code, and may transmit the codeword over a wireless channel. Areceiver, such as a user equipment (UE), may receive the codeword overthe wireless channel, select the bit index reliability sequence based ona length of the codeword, and decode the codeword based on the bit indexreliability sequence.

A method of wireless communication is described. The method may includereceiving a codeword over a wireless channel, where the codeword isbased on multiple information bits encoded using a polar code havingmultiple bit channels, identifying a set of bit locations of themultiple bit channels of the polar code for the multiple informationbits based on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe multiple bit channels that applies multiple weighting factors, anddecoding the received codeword according to the polar code to obtain aninformation bit vector at the set of bit locations.

An apparatus for wireless communication is described. The apparatus mayinclude means for receiving a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels, means for identifying a set of bitlocations of the multiple bit channels of the polar code for themultiple information bits based on a bit index reliability sequence,where the bit index reliability sequence is determined based on a binarybit weighting for the multiple bit channels that applies multipleweighting factors, and means for decoding the received codewordaccording to the polar code to obtain an information bit vector at theset of bit locations.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to receive a codeword over a wirelesschannel, where the codeword is based on multiple information bitsencoded using a polar code having multiple bit channels, identify a setof bit locations of the multiple bit channels of the polar code for themultiple information bits based on a bit index reliability sequence,where the bit index reliability sequence is determined based on a binarybit weighting for the multiple bit channels that applies multipleweighting factors, and decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to receive a codeword over awireless channel, where the codeword is based on multiple informationbits encoded using a polar code having multiple bit channels, identify aset of bit locations of the multiple bit channels of the polar code forthe multiple information bits based on a bit index reliability sequence,where the bit index reliability sequence is determined based on a binarybit weighting for the multiple bit channels that applies multipleweighting factors, and decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined by: performing the binary bit weighting usinga first weighting factor to obtain a first reliability sequence for themultiple bit channels. Some examples of the method, apparatus, andnon-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for modifying asubset of the first reliability sequence by performing the binary bitweighting using a second weighting factor to obtain a second reliabilitysequence for the subset of the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined by: modifying a subset of the secondreliability sequence by performing the binary bit weighting using athird weighting factor to obtain a third reliability sequence for thesubset of the second reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the subset of the firstreliability sequence includes the multiple bit channels having lowestbit-channel indices in the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the subset of the firstreliability sequence includes the multiple bit channels having highestbit-channel indices in the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined by: performing the binary bit weighting usinga first weighting factor for a first subset of bit indices and a secondweighting factor for a second subset of bit indices.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined by: performing the binary bit weighting usinga third weighting factor for a third subset of bit indices.

A method of wireless communication is described. The method may includeidentifying multiple information bits for encoding using a polar codehaving multiple bit channels, identifying a set of bit locations of themultiple bit channels of the polar code for the multiple informationbits based on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe multiple bit channels that applies multiple weighting factors,generating a codeword according to the polar code based on the bit indexreliability sequence and the multiple information bits, and transmittingthe codeword.

An apparatus for wireless communication is described. The apparatus mayinclude means for identifying multiple information bits for encodingusing a polar code having multiple bit channels, means for identifying aset of bit locations of the multiple bit channels of the polar code forthe multiple information bits based on a bit index reliability sequence,where the bit index reliability sequence is determined based on a binarybit weighting for the multiple bit channels that applies multipleweighting factors, means for generating a codeword according to thepolar code based on the bit index reliability sequence and the multipleinformation bits, and means for transmitting the codeword.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to identify multiple information bitsfor encoding using a polar code having multiple bit channels, identify aset of bit locations of the multiple bit channels of the polar code forthe multiple information bits based on a bit index reliability sequence,where the bit index reliability sequence is determined based on a binarybit weighting for the multiple bit channels that applies multipleweighting factors, generate a codeword according to the polar code basedon the bit index reliability sequence and the multiple information bits,and transmit the codeword.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to identify multipleinformation bits for encoding using a polar code having multiple bitchannels, identify a set of bit locations of the multiple bit channelsof the polar code for the multiple information bits based on a bit indexreliability sequence, where the bit index reliability sequence isdetermined based on a binary bit weighting for the multiple bit channelsthat applies multiple weighting factors, generate a codeword accordingto the polar code based on the bit index reliability sequence and themultiple information bits, and transmit the codeword.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined based on performing the binary bit weightingusing a first weighting factor to obtain a first reliability sequencefor the multiple bit channels. Some examples of the method, apparatus,and non-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for modifying asubset of the first reliability sequence by performing the binary bitweighting using a second weighting factor to obtain a second reliabilitysequence for the subset of the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined based on modifying a subset of the secondreliability sequence by performing the binary bit weighting using athird weighting factor to obtain a third reliability sequence for thesubset of the second reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the subset of the firstreliability sequence includes the multiple bit channels having lowestbit-channel indices in the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the subset of the firstreliability sequence includes the multiple bit channels having highestbit-channel indices in the first reliability sequence.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined based on performing the binary bit weightingusing a first weighting factor for a first subset of bit indices and asecond weighting factor for a second subset of bit indices.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the bit index reliabilitysequence may be determined based on performing the binary bit weightingusing a third weighting factor for a third subset of bit indices.

A method of wireless communication is described. The method may includereceiving a codeword over a wireless channel, where the codeword isbased on multiple information bits encoded using a polar code havingmultiple bit channels, selecting a bit index reliability sequence forthe multiple bit channels based on a length of the codeword, where anorder of bit indices in the bit index reliability sequence is determinedbased on applying a UPO to an input search sequence to obtain a partialorder, applying an analytical method to obtain calculated relativeorders of bit indices not ordered in the partial order, and applying asimulation to refine an order of at least two bit indices selected basedon the calculated relative orders, and decoding the codeword based onthe bit index reliability sequence.

An apparatus for wireless communication is described. The apparatus mayinclude means for receiving a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels, means for selecting a bit indexreliability sequence for the multiple bit channels based on a length ofthe codeword, where an order of bit indices in the bit index reliabilitysequence is determined based on applying a UPO to an input searchsequence to obtain a partial order, applying an analytical method toobtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders, andmeans for decoding the codeword based on the bit index reliabilitysequence.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to receive a codeword over a wirelesschannel, where the codeword is based on multiple information bitsencoded using a polar code having multiple bit channels, select a bitindex reliability sequence for the multiple bit channels based on alength of the codeword, where an order of bit indices in the bit indexreliability sequence is determined based on applying a UPO to an inputsearch sequence to obtain a partial order, applying an analytical methodto obtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders, anddecode the codeword based on the bit index reliability sequence.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to receive a codeword over awireless channel, where the codeword is based on multiple informationbits encoded using a polar code having multiple bit channels, select abit index reliability sequence for the multiple bit channels based on alength of the codeword, where an order of bit indices in the bit indexreliability sequence is determined based on applying a UPO to an inputsearch sequence to obtain a partial order, applying an analytical methodto obtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders, anddecode the codeword based on the bit index reliability sequence.

A memory of an apparatus for wireless communication is described.Instructions may be stored in the memory and operable, when executed bya processor of the apparatus, to cause the apparatus to receive, over awireless channel, a codeword that is based on a set of information bitsencoded using a polar code having a set of bit channels, select a bitindex reliability sequence for the set of bit channels based on a lengthof the codeword, and decode the codeword based on a bit indexreliability sequence, wherein an order of bit indices in the bit indexreliability sequence is determined by a process that includes applying aUPO to an input search sequence to obtain a partial order, applying ananalytical method to obtain calculated relative orders of bit indicesnot ordered in the partial order, and applying a simulation to refine anorder of at least two bit indices selected based on the calculatedrelative orders.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,decoding the codeword includes: applying successive cancellation listdecoding algorithm to a signal that includes the codeword.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,the simulation may be based on a list size applied by the successivecancellation list decoding algorithm.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,the simulation may be a link-level performance simulation.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,the analytical method may be an index polarization weight rule, or aReed-Muller rule, or a density evolution (DE) rule, or a mutualinformation-DE (MI-DE) rule, or any combination thereof.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,the order of bit indices in the reliability sequence may be determinedbased on: selecting a bit index from the input search sequence based onthe partial order. Some examples of the method, apparatus,non-transitory computer-readable medium, and memory of an apparatusdescribed above may further include processes, features, means, orinstructions for adding the selected bit index to the bit indexreliability sequence.

Some examples of the method, apparatus, non-transitory computer-readablemedium, and memory of an apparatus described above may further includeprocesses, features, means, or instructions for removing the selectedbit index from the input search sequence to generate an input searchsubsequence. Some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above mayfurther include processes, features, means, or instructions forcalculating a second partial order under the UPO of the input searchsubsequence. Some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above mayfurther include processes, features, means, or instructions forselecting a bit index from the input search subsequence based on thesecond partial order.

In some examples of the method, apparatus, non-transitorycomputer-readable medium, and memory of an apparatus described above,the UPO includes a first property and a second property, where thecalculated relative orders of bit indices violates at least one of thefirst property or the second property.

Some examples of the method, apparatus, non-transitory computer-readablemedium, and memory of an apparatus described above may further includeprocesses, features, means, or instructions for modifying a portion ofthe bit index reliability sequence using a second sequence to generate amodified bit index reliability sequence, where decoding the codewordincludes: decoding the codeword based on the modified bit indexreliability sequence.

A method of wireless communication is described. The method may includedetermining a bit index reliability sequence for multiple bit channelsof a polar code based on a length of a codeword, where an order of bitindices in the reliability sequence is determined based on applying aUPO to an input search sequence to obtain a partial order, applying ananalytical method to obtain calculated relative orders of bit indicesnot ordered in the partial order, and applying a simulation to refine anorder of at least two bit indices selected based on the calculatedrelative orders, generating the codeword according to the polar codebased on the bit index reliability sequence and multiple informationbits encoded using the polar code, and transmitting the codeword.

An apparatus for wireless communication is described. The apparatus mayinclude means for determining a bit index reliability sequence formultiple bit channels of a polar code based on a length of a codeword,where an order of bit indices in the reliability sequence is determinedbased on applying a UPO to an input search sequence to obtain a partialorder, applying an analytical method to obtain calculated relativeorders of bit indices not ordered in the partial order, and applying asimulation to refine an order of at least two bit indices selected basedon the calculated relative orders, means for generating the codewordaccording to the polar code based on the bit index reliability sequenceand multiple information bits encoded using the polar code, and meansfor transmitting the codeword.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to determine a bit index reliabilitysequence for multiple bit channels of a polar code based on a length ofa codeword, where an order of bit indices in the reliability sequence isdetermined based on applying a UPO to an input search sequence to obtaina partial order, applying an analytical method to obtain calculatedrelative orders of bit indices not ordered in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated relative orders, generate the codewordaccording to the polar code based on the bit index reliability sequenceand multiple information bits encoded using the polar code, and transmitthe codeword.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to determine a bit indexreliability sequence for multiple bit channels of a polar code based ona length of a codeword, where an order of bit indices in the reliabilitysequence is determined based on applying a UPO to an input searchsequence to obtain a partial order, applying an analytical method toobtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders,generate the codeword according to the polar code based on the bit indexreliability sequence and multiple information bits encoded using thepolar code, and transmit the codeword.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the simulation may be alink-level performance simulation.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the analytical method includesan index polarization weight rule, or a Reed-Muller rule, or a DE rule,or an MI-DE rule, or any combination thereof.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the order of bit indices inthe bit index reliability sequence is further determined based onselecting a bit index from the input search sequence based on thepartial order. Some examples of the method, apparatus, andnon-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for adding theselected bit index to the bit index reliability sequence.

Some examples of the method, apparatus, and non-transitorycomputer-readable medium described above may further include processes,features, means, or instructions for removing the selected bit indexfrom the input search sequence to generate an input search subsequence,calculating a second partial order under the UPO of the input searchsubsequence, and selecting a bit index from the input search subsequencebased on the second partial order.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the UPO includes a firstproperty and a second property, where the calculated relative orders ofbit indices violates at least one of the first property or the secondproperty.

Some examples of the method, apparatus, and non-transitorycomputer-readable medium described above may further include processes,features, means, or instructions for modifying a portion of the bitindex reliability sequence using a second sequence to generate amodified bit index reliability sequence, where generating the codewordincludes generating the codeword based on the modified bit indexreliability sequence.

Described techniques improve bit allocation at a quantization boundary.Bit channels of a polar code may be recursively partition at one or morepolarization stages of the polar code using a baseline rate allocationrule. The baseline rate allocation rule may have ceiling and flooroperations that control the number of information bits to allocate to apartition. At the quantization boundary, a bit may be allocated to oneof multiple partitions. One or more quantization rules may be appliedfor determining whether to assign a number of bits to a bit channelpartition to a fixed value. In some examples, assigning information bitsto a partition may be adjusted to be compliant with a UPO.

In some examples, a transmitter, such as a base station or a userequipment, may identify a set of bit locations of a polar code for a setof information bits. The set of bit locations may be determined based ona recursive partitioning of a set of bit channels of the polar code forat least a subset of polarization stages of the polar code. For eachpartition of the at least the subset of the polarization stages of thepolar code, portions of a number of the information bits of eachpartition may be assigned to bit channel sub-partitions. In someexamples, at least one quantization rule may be applied for determiningwhether to assign a first number of the information bits of a first bitchannel sub-partition of the bit channel sub-partitions to a fixedvalue. In some examples, assigning portions of a number of theinformation bits of each partition to bit channel sub-partitions mayinclude adjusting the information bit allocation derived based on therecursive partitioning to be compliant with a UPO. The transmitter mayencode a codeword according to the polar code based on the set of bitlocations, and transmit the encoded codeword over the wireless channel.A receiver, such as a base station or a user equipment, may receive thecodeword over the wireless channel, identify the set of bit locations ofthe polar code for a set of information bits, and decode the receivedcodeword according to the polar code to obtain an information bit vectorat the set of bit locations.

A method of wireless communication is described. The method may includeencoding a codeword using a polar code for a transmission over awireless channel, where the codeword includes an information bit vectorincluding multiple information bits, identifying a set of bit locationsof the polar code for the multiple information bits, where the set ofbit locations is determined based on a recursive partitioning ofmultiple bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of each partition to bitchannel sub-partitions, where at least one quantization rule is appliedfor determining whether to assign a first number of the information bitsof a first bit channel sub-partition of the bit channel sub-partitionsto a fixed value, and transmitting the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations.

An apparatus for wireless communication is described. The apparatus mayinclude means for encoding a codeword using a polar code for atransmission over a wireless channel, where the codeword includes aninformation bit vector including multiple information bits, means foridentifying a set of bit locations of the polar code for the multipleinformation bits, where the set of bit locations is determined based ona recursive partitioning of multiple bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof each partition to bit channel sub-partitions, where at least onequantization rule is applied for determining whether to assign a firstnumber of the information bits of a first bit channel sub-partition ofthe bit channel sub-partitions to a fixed value, and means fortransmitting the encoded codeword over the wireless channel according tothe polar code based on the set of bit locations.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to encode a codeword using a polarcode for a transmission over a wireless channel, where the codewordincludes an information bit vector including multiple information bits,identify a set of bit locations of the polar code for the multipleinformation bits, where the set of bit locations is determined based ona recursive partitioning of multiple bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof each partition to bit channel sub-partitions, where at least onequantization rule is applied for determining whether to assign a firstnumber of the information bits of a first bit channel sub-partition ofthe bit channel sub-partitions to a fixed value, and transmit theencoded codeword over the wireless channel according to the polar codebased on the set of bit locations.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to encode a codeword using apolar code for a transmission over a wireless channel, where thecodeword includes an information bit vector including multipleinformation bits, identify a set of bit locations of the polar code forthe multiple information bits, where the set of bit locations isdetermined based on a recursive partitioning of multiple bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of each partition to bit channel sub-partitions,where at least one quantization rule is applied for determining whetherto assign a first number of the information bits of a first bit channelsub-partition of the bit channel sub-partitions to a fixed value, andtransmit the encoded codeword over the wireless channel according to thepolar code based on the set of bit locations.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, a first quantization rule ofthe at least one quantization rule sets the first number to the fixedvalue as a function of a capacity of the first bit channelsub-partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the first quantization ruleapplies a threshold that may be dependent on a number of bit channels ofeach partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the threshold may be selectedto maintain a UPO of the bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, a first quantization rule ofthe at least one quantization rule sets the first number to the fixedvalue as a function of a code rate of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the function may be selectedto maintain a UPO of the bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the fixed value may be afunction of a number of bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the fixed value may be equalto a number of bit channels of each partition.

Some examples of the method, apparatus, and non-transitorycomputer-readable medium described above may further include processes,features, means, or instructions for assigning, for a second partitionof the each partitions, a second number of information bits of thesecond partition a second bit channel sub-partition of the secondpartition based on a baseline allocation rule.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the baseline allocation ruleapplies a floor operation to a result of a function of a capacity of thesecond bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits may be less than or equal to the number of bit channels insub-partitions of the second partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the baseline allocation ruleapplies a ceiling operation to a result of a function of a capacity ofthe second bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits may be greater than the number of bit channels in sub-partitions ofthe second partition.

A method of wireless communication is described. The method may includeencoding a codeword using a polar code for a transmission over awireless channel, where the codeword includes an information bit vectorincluding multiple information bits, identifying a set of bit locationsof the polar code for the multiple information bits, where the set ofbit locations is determined based on a recursive partitioning ofmultiple bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of each partition to bitchannel sub-partitions by adjusting the information bit allocationderived based on the recursive partitioning to be compliant with a UPO,and transmitting the encoded codeword over the wireless channelaccording to the polar code based on the set of bit locations.

An apparatus for wireless communication is described. The apparatus mayinclude means for encoding a codeword using a polar code for atransmission over a wireless channel, where the codeword includes aninformation bit vector including multiple information bits, means foridentifying a set of bit locations of the polar code for the multipleinformation bits, where the set of bit locations is determined based ona recursive partitioning of multiple bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO, and means for transmitting the encodedcodeword over the wireless channel according to the polar code based onthe set of bit locations.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to encode a codeword using a polarcode for a transmission over a wireless channel, where the codewordincludes an information bit vector including multiple information bits,identify a set of bit locations of the polar code for the multipleinformation bits, where the set of bit locations is determined based ona recursive partitioning of multiple bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO, and transmit the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to encode a codeword using apolar code for a transmission over a wireless channel, where thecodeword includes an information bit vector including multipleinformation bits, identify a set of bit locations of the polar code forthe multiple information bits, where the set of bit locations isdetermined based on a recursive partitioning of multiple bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of each partition to bit channel sub-partitions byadjusting the information bit allocation derived based on the recursivepartitioning to be compliant with a UPO, and transmit the encodedcodeword over the wireless channel according to the polar code based onthe set of bit locations.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the adjusting the informationbit allocation includes: constructing a sequence for each partition thatmay be compliant with the UPO. Some examples of the method, apparatus,and non-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for generating a bitvector for assigning the number of the information bits according to amutual information (MI) recursion equation. Some examples of the method,apparatus, and non-transitory computer-readable medium described abovemay further include processes, features, means, or instructions forcomparing an order resulting from the bit vector to the UPO.

Some examples of the method, apparatus, and non-transitorycomputer-readable medium described above may further include processes,features, means, or instructions for determining, for a value of the bitvector for at least one of the each partitions, that the order resultingfrom the value of the bit vector violates the UPO. Some examples of themethod, apparatus, and non-transitory computer-readable medium describedabove may further include processes, features, means, or instructionsfor swapping the value of the bit vector with an adjacent value of thebit vector based on the identifying that the value violates the UPO.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the sequence may be determinedbased on a binary bit weighting for the bit channels of each partitionthat applies multiple weighting factors.

A method of wireless communication is described. The method may includereceiving a codeword over a wireless channel, where the codeword isbased on multiple information bits encoded using a polar code havingmultiple bit channels, identifying a set of bit locations of the polarcode for the multiple information bits, where the set of bit locationsis determined based on a recursive partitioning of multiple bit channelsof the polar code for at least a subset of polarization stages of thepolar code, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of each partition to bit channel sub-partitions,where at least one quantization rule is applied for determining whetherto assign a first number of the information bits of a first bit channelpartition of the bit channel partitions to a fixed value, and decodingthe received codeword according to the polar code to obtain aninformation bit vector at the set of bit locations.

An apparatus for wireless communication is described. The apparatus mayinclude means for receiving a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels, means for identifying a set of bitlocations of the polar code for the multiple information bits, where theset of bit locations is determined based on a recursive partitioning ofmultiple bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of each partition to bitchannel sub-partitions, where at least one quantization rule is appliedfor determining whether to assign a first number of the information bitsof a first bit channel partition of the bit channel partitions to afixed value, and means for decoding the received codeword according tothe polar code to obtain an information bit vector at the set of bitlocations.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to receive a codeword over a wirelesschannel, where the codeword is based on multiple information bitsencoded using a polar code having multiple bit channels, identify a setof bit locations of the polar code for the multiple information bits,where the set of bit locations is determined based on a recursivepartitioning of multiple bit channels of the polar code for at least asubset of polarization stages of the polar code, and, for each partitionof the at least the subset of the polarization stages of the polar code,assigning portions of a number of the information bits of each partitionto bit channel sub-partitions, where at least one quantization rule isapplied for determining whether to assign a first number of theinformation bits of a first bit channel partition of the bit channelpartitions to a fixed value, and decode the received codeword accordingto the polar code to obtain an information bit vector at the set of bitlocations.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to receive a codeword over awireless channel, where the codeword is based on multiple informationbits encoded using a polar code having multiple bit channels, identify aset of bit locations of the polar code for the multiple informationbits, where the set of bit locations is determined based on a recursivepartitioning of multiple bit channels of the polar code for at least asubset of polarization stages of the polar code, and, for each partitionof the at least the subset of the polarization stages of the polar code,assigning portions of a number of the information bits of each partitionto bit channel sub-partitions, where at least one quantization rule isapplied for determining whether to assign a first number of theinformation bits of a first bit channel partition of the bit channelpartitions to a fixed value, and decode the received codeword accordingto the polar code to obtain an information bit vector at the set of bitlocations.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, a first quantization rule ofthe at least one quantization rule sets the first number to the fixedvalue as a function of a capacity of the first bit channel partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the first quantization ruleapplies a threshold that may be dependent on a number of bit channels ofeach partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the threshold may be selectedto maintain a UPO of the bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, a first quantization rule ofthe at least one quantization rule sets the first number to the fixedvalue as a function of a code rate of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the function may be selectedto maintain a UPO of the bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the fixed value may be afunction of a number of bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the fixed value may be equalto a number of bit channels of each partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, for a second partition of eachpartitions, a second number of information bits of the second partitionmay be assigned to a second bit channel sub-partition of the secondpartition based on a baseline allocation rule.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the baseline allocation ruleapplies a floor operation to a result of a function of a capacity of thesecond bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits may be less than or equal to the number of bit channels insub-partitions of the second partition.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the baseline allocation ruleapplies a ceiling operation to a result of a function of a capacity ofthe second bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits may be greater than the number of bit channels in sub-partitions ofthe second partition.

A method of wireless communication is described. The method may includereceiving a codeword over a wireless channel, where the codeword isbased on multiple information bits encoded using a polar code havingmultiple bit channels, identifying a set of bit locations of the polarcode for the multiple information bits, where the set of bit locationsis determined based on a recursive partitioning of multiple bit channelsof the polar code for at least a subset of polarization stages of thepolar code, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of each partition to bit channel sub-partitions byadjusting the information bit allocation derived based on the recursivepartitioning to be compliant with a UPO, and decoding the receivedcodeword according to the polar code to obtain an information bit vectorat the set of bit locations.

An apparatus for wireless communication is described. The apparatus mayinclude means for receiving a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels, means for identifying a set of bitlocations of the polar code for the multiple information bits, where theset of bit locations is determined based on a recursive partitioning ofmultiple bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of each partition to bitchannel sub-partitions by adjusting the information bit allocationderived based on the recursive partitioning to be compliant with a UPO,and means for decoding the received codeword according to the polar codeto obtain an information bit vector at the set of bit locations.

Another apparatus for wireless communication is described. The apparatusmay include a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to receive a codeword over a wirelesschannel, where the codeword is based on multiple information bitsencoded using a polar code having multiple bit channels, identify a setof bit locations of the polar code for the multiple information bits,where the set of bit locations is determined based on a recursivepartitioning of multiple bit channels of the polar code for at least asubset of polarization stages of the polar code, and, for each partitionof the at least the subset of the polarization stages of the polar code,assigning portions of a number of the information bits of each partitionto bit channel sub-partitions by adjusting the information bitallocation derived based on the recursive partitioning to be compliantwith a UPO, and decode the received codeword according to the polar codeto obtain an information bit vector at the set of bit locations.

A non-transitory computer readable medium for wireless communication isdescribed. The non-transitory computer-readable medium may includeinstructions operable to cause a processor to receive a codeword over awireless channel, where the codeword is based on multiple informationbits encoded using a polar code having multiple bit channels, identify aset of bit locations of the polar code for the multiple informationbits, where the set of bit locations is determined based on a recursivepartitioning of multiple bit channels of the polar code for at least asubset of polarization stages of the polar code, and, for each partitionof the at least the subset of the polarization stages of the polar code,assigning portions of a number of the information bits of each partitionto bit channel sub-partitions by adjusting the information bitallocation derived based on the recursive partitioning to be compliantwith a UPO, and decode the received codeword according to the polar codeto obtain an information bit vector at the set of bit locations.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the adjusting the informationbit allocation includes: constructing a sequence for each partition thatmay be compliant with the UPO. Some examples of the method, apparatus,and non-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for generating a bitvector for assigning the number of the information bits according to anMI recursion equation. Some examples of the method, apparatus, andnon-transitory computer-readable medium described above may furtherinclude processes, features, means, or instructions for comparing anorder resulting from the bit vector to the UPO.

Some examples of the method, apparatus, and non-transitorycomputer-readable medium described above may further include processes,features, means, or instructions for determining, for a value of the bitvector for at least one of the each partitions, that the order resultingfrom the value of the bit vector violates the UPO. Some examples of themethod, apparatus, and non-transitory computer-readable medium describedabove may further include processes, features, means, or instructionsfor swapping the value of the bit vector with an adjacent value of thebit vector based on the identifying that the value violates the UPO.

In some examples of the method, apparatus, and non-transitorycomputer-readable medium described above, the sequence may be determinedbased on a binary bit weighting for the bit channels of each partitionthat applies multiple weighting factors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a wireless communications system thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 2 illustrates an example of a wireless communications system thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 3 illustrates an example of a polar encoder that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 4 illustrates an example of a polar coding scheme that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 5 illustrates an example of polar code bit sequence generation thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 6 illustrates an example of a Hasse diagram that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 7 illustrates an example of a wireless communications system thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 8 illustrates an example of a polar code construction scheme thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 9 illustrates an example of a polar code construction scheme thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 10 illustrates an example of a polar code construction scheme thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIG. 11 illustrates an example of a bit sequence reordering diagram thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIGS. 12 through 14 show block diagrams of a device that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 15 illustrates a block diagram of a system including a base stationthat supports information bit distribution design in accordance withaspects of the present disclosure.

FIGS. 16 through 18 show block diagrams of a device that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 19 illustrates a block diagram of a system including a userequipment (UE) that supports information bit distribution design inaccordance with aspects of the present disclosure.

FIGS. 20 through 25 illustrate methods for information bit distributiondesign in accordance with aspects of the present disclosure.

FIGS. 26 through 28 show block diagrams of a device that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 29 illustrates a block diagram of a system including a UE thatsupports information bit distribution design in accordance with aspectsof the present disclosure.

FIGS. 30 through 32 show block diagrams of a device that supportsinformation bit distribution design in accordance with aspects of thepresent disclosure.

FIG. 33 illustrates a block diagram of a system including a base stationthat supports information bit distribution design in accordance withaspects of the present disclosure.

FIGS. 34 through 37 illustrate methods for information bit distributiondesign in accordance with aspects of the present disclosure.

DETAILED DESCRIPTION

The described techniques relate to improved methods, systems, devices,apparatuses, or products by processes that support polar sequence designbased on coefficient reliability and improved information bitdistribution for polar codes. Generally, the described techniques mayprovide improved techniques for information bit distribution designand/or may improve bit allocation at a quantization boundary.

In some examples, bit channels of a polar code may be determined by auniversal partial order (UPO). However, some bit channels ordered by aUPO may have the same order and may not be comparable under current UPOrules. The techniques described herein may be applied by a device ormodule (e.g., a transmitter, a receiver, an encoder, a decoder, aprocess for creating a lookup table, or any combination of these) forselecting between at least two bit channel indices having a same orderunder the UPO. For instance, an analytical method or a simulation may beapplied to the two indices. Additionally or alternatively, the device ormodule may determine bit channels of a polar code based on a bit indexreliability sequence determined using hybrid polarization weightingfactors. For instance, the device or module may generate a sequence andweight the entire sequence or a portion of the sequence by a certainfactor. In some cases, the device or module may further weight a subsetof the sequence to produce the bit index reliability sequence.

In some examples, bit channels of a polar code may be recursivelypartitioned at one or more polarization stages of the polar code using abaseline rate allocation rule. The baseline rate allocation rule mayhave ceiling and floor operations that control the number of informationbits to allocate to a partition. At the quantization boundary, a bit maybe allocated to one of multiple partitions. One or more quantizationrules may be applied for determining whether to assign a number of bitsof a bit channel partition to a fixed value. In some examples, assigninginformation bits to a partition may be adjusted to be compliant with aUPO.

A polar code may be composed of multiple channels having differentlevels of reliability. Channel reliability may represent a capacity ofthe channel to carry information as part of the encoded codeword.Channels of a polar code having higher reliabilities are used to encodeinformation bits and the remaining channels are used to encode frozenbits. A frozen bit is a bit having a known value to a decoder and isgenerally set as ‘0’. For N channels, K information bits may be loadedinto the K most reliable channels and N−K frozen bits may be loaded intothe N−K least reliable channels, where, in some cases, K<N.

A transmitter, such as a base station or a user equipment (UE), maydetermine a bit index reliability sequence for a set of bit channels ofa polar code based on a length of the codeword. An encoder (e.g., anencoder working in conjunction with the transmitter, a device generatinga lookup table for reliability sequences, etc.) may determine an orderof bit indices in the bit index reliability sequence based on hybridpolarization weighting factors. The encoder may apply the hybridpolarization weighting factors using nested sequence generation. Forexample, a first sequence may be generated for a given polar code length(e.g., N₁) using a first polarization weighting factor (e.g., β₁), and asubset of the sequence values may be replaced with a sequence of asecond length (e.g., N₂, where N₂<N₁) that is generated using a secondpolarization weighting factor (e.g., β₂). The subset of the sequencevalues may correspond to the lowest (e.g., the lowest N₂) sequencevalues or the highest (e.g., the highest N₂) sequence values in thefirst sequence. The encoder may nest additional sequences usingadditional polarization weighting factors. Additionally oralternatively, the encoder may apply hybrid bit index weighting factorsfor a polarization weight function. For example, for a polar code havingm bit positions (e.g., where N=2^(m−1)), a first weighting factor may beapplied for a first subset of the bit positions and a second weightingfactor may be applied for a second subset of the bit positions.

In some examples, an encoder may determine an order of bit indices in abit index reliability sequence based on applying a UPO to an inputsearch sequence to obtain a partial order. The encoder may additionallyapply an analytical method to obtain calculated relative orders of bitindices not ordered in the partial order, and may apply a simulation torefine an order of at least two bit indices selected based on thecalculated relative orders. The transmitter or encoder may generate thecodeword according to the polar code based on the bit index reliabilitysequence and a set of information bits encoded using the polar code, andthe transmitter may transmit the codeword over a wireless channel. Areceiver, such as a UE or base station, may receive the codeword overthe wireless channel, select the bit index reliability sequence based ona length of the codeword, and decode the codeword based on the bit indexreliability sequence.

In some examples, a transmitter, such as a base station or a UE, mayidentify a set of bit locations of a polar code for a set of informationbits based on recursive partitioning for at least a subset ofpolarization stages of the polar code. For each partition of the subsetof polarization stages of the polar code, portions of a number of theinformation bits of each partition may be assigned to bit channelsub-partitions. In some examples, at least one quantization rule may beapplied for determining whether to assign a first number of theinformation bits of a first bit channel sub-partition of the bit channelsub-partitions to a fixed value. In some examples, assigning portions ofa number of the information bits of each partition to bit channelsub-partitions may include adjusting the information bit allocationderived based on the recursive partitioning to be compliant with a UPO.The transmitter may encode a codeword according to the polar code basedon the set of bit locations, and may transmit the encoded codeword overthe wireless channel. A receiver, such as a base station or a UE, mayreceive the codeword over the wireless channel, identify the set of bitlocations of the polar code for a set of information bits, and decodethe received codeword according to the polar code to obtain aninformation bit vector at the set of bit locations.

Aspects of the disclosure are initially described in the context of awireless communications system. The wireless communications system mayidentify a reliability order for channels of a polar code. The wirelesscommunications system may also identify a number of information bits foreach partition at each stage of polarization. Aspects of the disclosureare further illustrated by and described with reference to apparatusdiagrams, system diagrams, and flowcharts that relate to information bitdistribution design.

FIG. 1 illustrates an example of a wireless communications system 100 inaccordance with various aspects of the present disclosure. The wirelesscommunications system 100 includes base stations 105, UEs 115, and acore network 130. In some examples, the wireless communications system100 may be a Long Term Evolution (LTE) network, an LTE-Advanced (LTE-A)network, or a New Radio (NR) network. In some cases, wirelesscommunications system 100 may support enhanced broadband communications,ultra-reliable (e.g., mission critical) communications, low latencycommunications, or communications with low-cost and low-complexitydevices.

Base stations 105 may wirelessly communicate with UEs 115 via one ormore base station antennas. Base stations 105 described herein mayinclude or may be referred to by those skilled in the art as a basetransceiver station, a radio base station, an access point, a radiotransceiver, a NodeB, an eNodeB (eNB), a next-generation Node B orgiga-nodeB (either of which may be referred to as a gNB), a Home NodeB,a Home eNodeB, or some other suitable terminology. Wirelesscommunications system 100 may include base stations 105 of differenttypes (e.g., macro or small cell base stations). The UEs 115 describedherein may be able to communicate with various types of base stations105 and network equipment including macro eNBs, small cell eNBs, gNBs,relay base stations, and the like.

Each base station 105 may be associated with a particular geographiccoverage area 110 in which communications with various UEs 115 issupported. Each base station 105 may provide communication coverage fora respective geographic coverage area 110 via communication links 125,and communication links 125 between a base station 105 and a UE 115 mayutilize one or more carriers. Communication links 125 shown in wirelesscommunications system 100 may include uplink transmissions from a UE 115to a base station 105, or downlink transmissions, from a base station105 to a UE 115. Downlink transmissions may also be called forward linktransmissions while uplink transmissions may also be called reverse linktransmissions.

The geographic coverage area 110 for a base station 105 may be dividedinto sectors making up only a portion of the geographic coverage area110, and each sector may be associated with a cell. For example, eachbase station 105 may provide communication coverage for a macro cell, asmall cell, a hot spot, or other types of cells, or various combinationsthereof. In some examples, a base station 105 may be movable andtherefore provide communication coverage for a moving geographiccoverage area 110. In some examples, different geographic coverage areas110 associated with different technologies may overlap and overlappinggeographic coverage areas 110 associated with different technologies maybe supported by the same base station 105 or by different base stations105. The wireless communications system 100 may include, for example, aheterogeneous LTE/LTE-A or NR network in which different types of basestations 105 provide coverage for various geographic coverage areas 110.

The term “cell” refers to a logical communication entity used forcommunication with a base station 105 (e.g., over a carrier), and may beassociated with an identifier for distinguishing neighboring cells(e.g., a physical cell identifier (PCID), a virtual cell identifier(VCID)) operating via the same or a different carrier. In some examples,a carrier may support multiple cells, and different cells may beconfigured according to different protocol types (e.g., machine-typecommunication (MTC), narrowband Internet-of-Things (NB-IoT), enhancedmobile broadband (eMBB), or others) that may provide access fordifferent types of devices. In some cases, the term “cell” may refer toa portion of a geographic coverage area 110 (e.g., a sector) over whichthe logical entity operates.

UEs 115 may be dispersed throughout the wireless communications system100, and each UE 115 may be stationary or mobile. A UE 115 may also bereferred to as a mobile device, a wireless device, a remote device, ahandheld device, or a subscriber device, or some other suitableterminology, where the “device” may also be referred to as a unit, astation, a terminal, or a client. A UE 115 may also be a personalelectronic device such as a cellular phone, a personal digital assistant(PDA), a tablet computer, a laptop computer, or a personal computer. Insome examples, a UE 115 may also refer to a wireless local loop (WLL)station, an Internet of Things (IoT) device, an Internet of Everything(IoE) device, or an MTC device, or the like, which may be implemented invarious articles such as appliances, vehicles, meters, or the like.

Some UEs 115, such as MTC or IoT devices, may be low cost or lowcomplexity devices, and may provide for automated communication betweenmachines (e.g., via Machine-to-Machine (M2M) communication). M2Mcommunication or MTC may refer to data communication technologies thatallow devices to communicate with one another or a base station 105without human intervention. In some examples, M2M communication or MTCmay include communications from devices that integrate sensors or metersto measure or capture information and relay that information to acentral server or application program that can make use of theinformation or present the information to humans interacting with theprogram or application. Some UEs 115 may be designed to collectinformation or enable automated behavior of machines. Examples ofapplications for MTC devices include smart metering, inventorymonitoring, water level monitoring, equipment monitoring, healthcaremonitoring, wildlife monitoring, weather and geological eventmonitoring, fleet management and tracking, remote security sensing,physical access control, and transaction-based business charging.

Some UEs 115 may be configured to employ operating modes that reducepower consumption, such as half-duplex communications (e.g., a mode thatsupports one-way communication via transmission or reception, but nottransmission and reception simultaneously). In some examples half-duplexcommunications may be performed at a reduced peak rate. Other powerconservation techniques for UEs 115 include entering a power saving“deep sleep” mode when not engaging in active communications, oroperating over a limited bandwidth (e.g., according to narrowbandcommunications). In some cases, UEs 115 may be designed to supportcritical functions (e.g., mission critical functions), and a wirelesscommunications system 100 may be configured to provide ultra-reliablecommunications for these functions.

In some cases, a UE 115 may also be able to communicate directly withother UEs 115 (e.g., using a peer-to-peer (P2P) or device-to-device(D2D) protocol). One or more of a group of UEs 115 utilizing D2Dcommunications may be within the geographic coverage area 110 of a basestation 105. Other UEs 115 in such a group may be outside the geographiccoverage area 110 of a base station 105 or be otherwise unable toreceive transmissions from a base station 105. In some cases, groups ofUEs 115 communicating via D2D communications may utilize a one-to-many(1:M) system in which each UE 115 transmits to every other UE 115 in thegroup. In some cases, a base station 105 facilitates the scheduling ofresources for D2D communications. In other cases, D2D communications arecarried out between UEs 115 without the involvement of a base station105.

Base stations 105 may communicate with the core network 130 and with oneanother. For example, base stations 105 may interface with the corenetwork 130 through backhaul links 132 (e.g., via an S1 or otherinterface). Base stations 105 may communicate with one another overbackhaul links 134 (e.g., via an X2 or other interface) either directly(e.g., directly between base stations 105) or indirectly (e.g., via corenetwork 130).

The core network 130 may provide user authentication, accessauthorization, tracking, Internet Protocol (IP) connectivity, and otheraccess, routing, or mobility functions. The core network 130 may be anevolved packet core (EPC), which may include at least one mobilitymanagement entity (MME), at least one serving gateway (S-GW), and atleast one Packet Data Network (PDN) gateway (P-GW). The MME may managenon-access stratum (e.g., control plane) functions such as mobility,authentication, and bearer management for UEs 115 served by basestations 105 associated with the EPC. User IP packets may be transferredthrough the S-GW, which itself may be connected to the P-GW. The P-GWmay provide IP address allocation as well as other functions. The P-GWmay be connected to the network operators IP services. The operators IPservices may include access to the Internet, Intranet(s), an IPMultimedia Subsystem (IMS), or a Packet-Switched (PS) Streaming Service.

At least some of the network devices, such as a base station 105, mayinclude subcomponents such as an access network entity, which may be anexample of an access node controller (ANC). Each access network entitymay communicate with UEs 115 through a number of other access networktransmission entities, which may be referred to as a radio head, a smartradio head, or a transmission/reception point (TRP). In someconfigurations, various functions of each access network entity or basestation 105 may be distributed across various network devices (e.g.,radio heads and access network controllers) or consolidated into asingle network device (e.g., a base station 105).

Wireless communications system 100 may operate using one or morefrequency bands, typically in the range of 300 MHz to 300 GHz.Generally, the region from 300 MHz to 3 GHz is known as the ultra-highfrequency (UHF) region or decimeter band, since the wavelengths rangefrom approximately one decimeter to one meter in length. UHF waves maybe blocked or redirected by buildings and environmental features.However, the waves may penetrate structures sufficiently for a macrocell to provide service to UEs 115 located indoors. Transmission of UHFwaves may be associated with smaller antennas and shorter range (e.g.,less than 100 km) compared to transmission using the smaller frequenciesand longer waves of the high frequency (HF) or very high frequency (VHF)portion of the spectrum below 300 MHz.

Wireless communications system 100 may also operate in a super highfrequency (SHF) region using frequency bands from 3 GHz to 30 GHz, alsoknown as the centimeter band. The SHF region includes bands such as the5 GHz industrial, scientific, and medical (ISM) bands, which may be usedopportunistically by devices that can tolerate interference from otherusers.

Wireless communications system 100 may also operate in an extremely highfrequency (EHF) region of the spectrum (e.g., from 30 GHz to 300 GHz),also known as the millimeter band. In some examples, wirelesscommunications system 100 may support millimeter wave (mmW)communications between UEs 115 and base stations 105, and EHF antennasof the respective devices may be even smaller and more closely spacedthan UHF antennas. In some cases, this may facilitate use of antennaarrays within a UE 115. However, the propagation of EHF transmissionsmay be subject to even greater atmospheric attenuation and shorter rangethan SHF or UHF transmissions. Techniques disclosed herein may beemployed across transmissions that use one or more different frequencyregions, and designated use of bands across these frequency regions maydiffer by country or regulating body.

In some cases, wireless communications system 100 may utilize bothlicensed and unlicensed radio frequency spectrum bands. For example,wireless communications system 100 may employ License Assisted Access(LAA), LTE-Unlicensed (LTE-U) radio access technology, or NR technologyin an unlicensed band such as the 5 GHz ISM band. When operating inunlicensed radio frequency spectrum bands, wireless devices such as basestations 105 and UEs 115 may employ listen-before-talk (LBT) proceduresto ensure a frequency channel is clear before transmitting data. In somecases, operations in unlicensed bands may be based on a CA configurationin conjunction with CCs operating in a licensed band (e.g., LAA).Operations in unlicensed spectrum may include downlink transmissions,uplink transmissions, peer-to-peer transmissions, or a combination ofthese. Duplexing in unlicensed spectrum may be based on frequencydivision duplexing (FDD), time division duplexing (TDD), or acombination of both.

In some examples, base station 105 or UE 115 may be equipped withmultiple antennas, which may be used to employ techniques such astransmit diversity, receive diversity, multiple-input multiple-output(MIMO) communications, or beamforming. For example, wirelesscommunications system may use a transmission scheme between atransmitting device (e.g., a base station 105) and a receiving device(e.g., a UE 115), where the transmitting device is equipped withmultiple antennas and the receiving devices are equipped with one ormore antennas. MIMO communications may employ multipath signalpropagation to increase the spectral efficiency by transmitting orreceiving multiple signals via different spatial layers, which may bereferred to as spatial multiplexing. The multiple signals may, forexample, be transmitted by the transmitting device via differentantennas or different combinations of antennas. Likewise, the multiplesignals may be received by the receiving device via different antennasor different combinations of antennas. Each of the multiple signals maybe referred to as a separate spatial stream and may carry bitsassociated with the same data stream (e.g., the same codeword) ordifferent data streams. Different spatial layers may be associated withdifferent antenna ports used for channel measurement and reporting. MIMOtechniques include single-user MIMO (SU-MIMO) where multiple spatiallayers are transmitted to the same receiving device, and multiple-userMIMO (MU-MIMO) where multiple spatial layers are transmitted to multipledevices.

Beamforming, which may also be referred to as spatial filtering,directional transmission, or directional reception, is a signalprocessing technique that may be used at a transmitting device or areceiving device (e.g., a base station 105 or a UE 115) to shape orsteer an antenna beam (e.g., a transmit beam or receive beam) along aspatial path between the transmitting device and the receiving device.Beamforming may be achieved by combining the signals communicated viaantenna elements of an antenna array such that signals propagating atparticular orientations with respect to an antenna array experienceconstructive interference while others experience destructiveinterference. The adjustment of signals communicated via the antennaelements may include a transmitting device or a receiving deviceapplying certain amplitude and phase offsets to signals carried via eachof the antenna elements associated with the device. The adjustmentsassociated with each of the antenna elements may be defined by abeamforming weight set associated with a particular orientation (e.g.,with respect to the antenna array of the transmitting device orreceiving device, or with respect to some other orientation).

In one example, a base station 105 may use multiple antennas or antennaarrays to conduct beamforming operations for directional communicationswith a UE 115. For instance, some signals (e.g. synchronization signals,reference signals, beam selection signals, or other control signals) maybe transmitted by a base station 105 multiple times in differentdirections, which may include a signal being transmitted according todifferent beamforming weight sets associated with different directionsof transmission. Transmissions in different beam directions may be usedto identify (e.g., by the base station 105 or a receiving device, suchas a UE 115) a beam direction for subsequent transmission and/orreception by the base station 105. Some signals, such as data signalsassociated with a particular receiving device, may be transmitted by abase station 105 in a single beam direction (e.g., a directionassociated with the receiving device, such as a UE 115). In someexamples, the beam direction associated with transmissions along asingle beam direction may be determined based at least in part on asignal that was transmitted in different beam directions. For example, aUE 115 may receive one or more of the signals transmitted by the basestation 105 in different directions, and the UE 115 may report to thebase station 105 an indication of the signal it received with a highestsignal quality, or an otherwise acceptable signal quality. Althoughthese techniques are described with reference to signals transmitted inone or more directions by a base station 105, a UE 115 may employsimilar techniques for transmitting signals multiple times in differentdirections (e.g., for identifying a beam direction for subsequenttransmission or reception by the UE 115), or transmitting a signal in asingle direction (e.g., for transmitting data to a receiving device).

A receiving device (e.g., a UE 115, which may be an example of a mmWreceiving device) may try multiple receive beams when receiving varioussignals from the base station 105, such as synchronization signals,reference signals, beam selection signals, or other control signals. Forexample, a receiving device may try multiple receive directions byreceiving via different antenna subarrays, by processing receivedsignals according to different antenna subarrays, by receiving accordingto different receive beamforming weight sets applied to signals receivedat multiple antenna elements of an antenna array, or by processingreceived signals according to different receive beamforming weight setsapplied to signals received at multiple antenna elements of an antennaarray, any of which may be referred to as “listening” according todifferent receive beams or receive directions. In some examples areceiving device may use a single receive beam to receive along a singlebeam direction (e.g., when receiving a data signal). The single receivebeam may be aligned in a beam direction determined based on listeningaccording to different receive beam directions (e.g., a beam directiondetermined to have a highest signal strength, highest signal-to-noiseratio, or otherwise acceptable signal quality based on listeningaccording to multiple beam directions).

In some cases, the antennas of a base station 105 or UE 115 may belocated within one or more antenna arrays, which may support MIMOoperations, or transmit or receive beamforming. For example, one or morebase station antennas or antenna arrays may be co-located at an antennaassembly, such as an antenna tower. In some cases, antennas or antennaarrays associated with a base station 105 may be located in diversegeographic locations. A base station 105 may have an antenna array witha number of rows and columns of antenna ports that the base station 105may use to support beamforming of communications with a UE 115.Likewise, a UE 115 may have one or more antenna arrays that may supportvarious MIMO or beamforming operations.

In some cases, wireless communications system 100 may be a packet-basednetwork that operate according to a layered protocol stack. In the userplane, communications at the bearer or Packet Data Convergence Protocol(PDCP) layer may be IP-based. A Radio Link Control (RLC) layer may insome cases perform packet segmentation and reassembly to communicateover logical channels. A Medium Access Control (MAC) layer may performpriority handling and multiplexing of logical channels into transportchannels. The MAC layer may also use hybrid automatic repeat request(HARQ) to provide retransmission at the MAC layer to improve linkefficiency. In the control plane, the Radio Resource Control (RRC)protocol layer may provide establishment, configuration, and maintenanceof an RRC connection between a UE 115 and a base station 105 or corenetwork 130 supporting radio bearers for user plane data. At thePhysical (PHY) layer, transport channels may be mapped to physicalchannels.

In some cases, UEs 115 and base stations 105 may support retransmissionsof data to increase the likelihood that data is received successfully.HARQ feedback is one technique of increasing the likelihood that data isreceived correctly over a communication link 125. HARQ may include acombination of error detection (e.g., using a cyclic redundancy check(CRC)), forward error correction (FEC), and retransmission (e.g.,automatic repeat request (ARQ)). HARQ may improve throughput at the MAClayer in poor radio conditions (e.g., signal-to-noise conditions). Insome cases, a wireless device may support same-slot HARQ feedback, wherethe device may provide HARQ feedback in a specific slot for datareceived in a previous symbol in the slot. In other cases, the devicemay provide HARQ feedback in a subsequent slot, or according to someother time interval.

Time intervals in LTE or NR may be expressed in multiples of a basictime unit, which may, for example, refer to a sampling period ofT_(s)=1/30,720,000 seconds. Time intervals of a communications resourcemay be organized according to radio frames each having a duration of 10milliseconds (ms), where the frame period may be expressed asT_(f)=307,200 T_(s). The radio frames may be identified by a systemframe number (SFN) ranging from 0 to 1023. Each frame may include 10subframes numbered from 0 to 9, and each subframe may have a duration of1 ms. A subframe may be further divided into 2 slots each having aduration of 0.5 ms, and each slot may contain 6 or 7 modulation symbolperiods (e.g., depending on the length of the cyclic prefix prepended toeach symbol period). Excluding the cyclic prefix, each symbol period maycontain 2048 sampling periods. In some cases, a subframe may be thesmallest scheduling unit of the wireless communications system 100 andmay be referred to as a transmission time interval (TTI). In othercases, a smallest scheduling unit of the wireless communications system100 may be shorter than a subframe or may be dynamically selected (e.g.,in bursts of shortened TTIs (sTTIs) or in selected component carriersusing sTTIs).

In some wireless communications systems, a slot may further be dividedinto multiple mini-slots containing one or more symbols. In someinstances, a symbol of a mini-slot or a mini-slot may be the smallestunit of scheduling. Each symbol may vary in duration depending on thesubcarrier spacing or frequency band of operation, for example. Further,some wireless communications systems may implement slot aggregation inwhich multiple slots or mini-slots are aggregated together and used forcommunication between a UE 115 and a base station 105.

The term “carrier” refers to a set of radio frequency spectrum resourceshaving a defined physical layer structure for supporting communicationsover a communication link 125. For example, a carrier of a communicationlink 125 may include a portion of a radio frequency spectrum band thatis operated according to physical layer channels for a given radioaccess technology. Each physical layer channel may carry user data,control information, or other signaling. A carrier may be associatedwith a pre-defined frequency channel (e.g., an E-UTRA absolute radiofrequency channel number (EARFCN)), and may be positioned according to achannel raster for discovery by UEs 115. Carriers may be downlink oruplink (e.g., in an FDD mode), or be configured to carry downlink anduplink communications (e.g., in a TDD mode). In some examples, signalwaveforms transmitted over a carrier may be made up of multiplesub-carriers (e.g., using multi-carrier modulation (MCM) techniques suchas orthogonal frequency division multiplexing (OFDM) or DFT-s-OFDM).

The organizational structure of the carriers may be different fordifferent radio access technologies (e.g., LTE, LTE-A, NR, etc.). Forexample, communications over a carrier may be organized according toTTIs or slots, each of which may include user data as well as controlinformation or signaling to support decoding the user data. A carriermay also include dedicated acquisition signaling (e.g., synchronizationsignals or system information, etc.) and control signaling thatcoordinates operation for the carrier. In some examples (e.g., in acarrier aggregation configuration), a carrier may also have acquisitionsignaling or control signaling that coordinates operations for othercarriers.

Physical channels may be multiplexed on a carrier according to varioustechniques. A physical control channel and a physical data channel maybe multiplexed on a downlink carrier, for example, using time divisionmultiplexing (TDM) techniques, frequency division multiplexing (FDM)techniques, or hybrid TDM-FDM techniques. In some examples, controlinformation transmitted in a physical control channel may be distributedbetween different control regions in a cascaded manner (e.g., between acommon control region or common search space and one or more UE-specificcontrol regions or UE-specific search spaces).

A carrier may be associated with a particular bandwidth of the radiofrequency spectrum, and in some examples the carrier bandwidth may bereferred to as a “system bandwidth” of the carrier or the wirelesscommunications system 100. For example, the carrier bandwidth may be oneof a number of predetermined bandwidths for carriers of a particularradio access technology (e.g., 1.4, 3, 5, 10, 15, 20, 40, or 80 MHz). Insome examples, each served UE 115 may be configured for operating overportions or all of the carrier bandwidth. In other examples, some UEs115 may be configured for operation using a narrowband protocol typethat is associated with a predefined portion or range (e.g., set ofsubcarriers or RBs) within a carrier (e.g., “in-band” deployment of anarrowband protocol type).

In a system employing MCM techniques, a resource element may consist ofone symbol period (e.g., a duration of one modulation symbol) and onesubcarrier, where the symbol period and subcarrier spacing are inverselyrelated. The number of bits carried by each resource element may dependon the modulation scheme (e.g., the order of the modulation scheme).Thus, the more resource elements that a UE 115 receives and the higherthe order of the modulation scheme, the higher the data rate may be forthe UE 115. In MIMO systems, a wireless communications resource mayrefer to a combination of a radio frequency spectrum resource, a timeresource, and a spatial resource (e.g., spatial layers), and the use ofmultiple spatial layers may further increase the data rate forcommunications with a UE 115.

Devices of the wireless communications system 100 (e.g., base stations105 or UEs 115) may have a hardware configuration that supportscommunications over a particular carrier bandwidth, or may beconfigurable to support communications over one of a set of carrierbandwidths. In some examples, the wireless communications system 100 mayinclude base stations 105 and/or UEs 115 that can support simultaneouscommunications via carriers associated with more than one differentcarrier bandwidth.

Wireless communications system 100 may support communication with a UE115 on multiple cells or carriers, a feature which may be referred to ascarrier aggregation (CA) or multi-carrier operation. A UE 115 may beconfigured with multiple downlink CCs and one or more uplink CCsaccording to a carrier aggregation configuration. Carrier aggregationmay be used with both FDD and TDD component carriers.

In some cases, wireless communications system 100 may utilize enhancedcomponent carriers (eCCs). An eCC may be characterized by one or morefeatures including wider carrier or frequency channel bandwidth, shortersymbol duration, shorter TTI duration, or modified control channelconfiguration. In some cases, an eCC may be associated with a carrieraggregation configuration or a dual connectivity configuration (e.g.,when multiple serving cells have a suboptimal or non-ideal backhaullink). An eCC may also be configured for use in unlicensed spectrum orshared spectrum (e.g., where more than one operator is allowed to usethe spectrum). An eCC characterized by wide carrier bandwidth mayinclude one or more segments that may be utilized by UEs 115 that arenot capable of monitoring the whole carrier bandwidth or are otherwiseconfigured to use a limited carrier bandwidth (e.g., to conserve power).

In some cases, an eCC may utilize a different symbol duration than otherCCs, which may include use of a reduced symbol duration as compared withsymbol durations of the other CCs. A shorter symbol duration may beassociated with increased spacing between adjacent subcarriers. Adevice, such as a UE 115 or base station 105, utilizing eCCs maytransmit wideband signals (e.g., according to frequency channel orcarrier bandwidths of 20, 40, 60, 80 MHz, etc.) at reduced symboldurations (e.g., 16.67 microseconds). A TTI in eCC may consist of one ormultiple symbol periods. In some cases, the TTI duration (that is, thenumber of symbol periods in a TTI) may be variable.

Wireless communications systems 100 such as an NR system may utilize anycombination of licensed, shared, and unlicensed spectrum bands, amongothers. The flexibility of eCC symbol duration and subcarrier spacingmay allow for the use of eCC across multiple spectrums. In someexamples, NR shared spectrum may increase spectrum utilization andspectral efficiency, specifically through dynamic vertical (e.g., acrossfrequency) and horizontal (e.g., across time) sharing of resources.

Wireless communications system 100 may support polar coding for reliablecodeword transmissions. For example, a transmitting device (e.g., a basestation 105 or UE 115) may determine a bit index reliability sequencefor bit channels of a polar code (e.g., based on a length of thecodeword). In a first example, the device may determine an order of bitindices in the bit index reliability sequence based on applying a UPO toan input search sequence to obtain a partial order and applying ananalytical method to obtain calculated relative orders of bit indicesnot ordered in the partial order. The device may apply a simulation torefine an order of bit indices selected based on the calculated relativeorders. In a second example, the device may determine the order of bitindices in the reliability sequence based on a lookup table, where thelookup table was generated or determined based on a process similar tothat described above. The device may generate the codeword for a set ofinformation bits according to the polar code based on the bit indexreliability sequence, and may transmit the codeword to a receivingdevice (e.g., a UE 115 or base station 105).

The receiving device may receive the codeword over the wireless channel(e.g., an uplink or downlink channel), and may decode the codewordaccording to the bit index reliability sequence. For example, thereceiving device may select the bit index reliability sequence based onthe length of the codeword. In a first example, the receiving device maydetermine an order of bit indices in the reliability sequence based onapplying a UPO to an input search sequence to obtain a partial order,applying an analytical method to obtain calculated relative orders ofbit indices not ordered in the partial order, and applying a simulationto refine an order of bit indices selected based on the calculatedrelative orders. In a second example, the receiving device may selectthe bit index reliability sequence from a lookup table based on thelength of the codeword, where the lookup table is generated ordetermined based on the above described steps.

FIG. 2 illustrates an example of a wireless communications system 200that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, wirelesscommunications system 200 may implement aspects of wirelesscommunications system 100. In the example of FIG. 2, base station 105-amay use polar encoding to encode information bits for transmission to UE115-a, which may be an example of a corresponding UE 115 as describedwith reference to FIG. 1, via a communication channel 235. In someexamples, UE 115-a may encode data for transmission to base station105-a, which may be an example of a corresponding base station 105 asdescribed with reference to FIG. 1, or to another UE 115 using thesesame techniques. In further examples, base station 105-a may encode datafor transmission to another base station 105 using these sametechniques. Moreover, devices other than base station 105-a and UE 115-amay use the techniques described herein for decoding a codeword encodedusing a polar code.

In the depicted example, base station 105-a may include a data source205, a transmitter sequence identifier 210, and a polar encoder 215. Thedata source 205 may provide an information vector of k information bitsto be encoded and transmitted to UE 115-a. The data source 205 may becoupled to a network, a storage device, or the like. The data source 205may output the information vector to the sequence identifier 210. Thetransmitter sequence identifier 210 may select a length N in bits of acodeword and a bit index reliability sequence corresponding to theselected length N. The transmitter sequence identifier 210 may outputthe k information bits, the length N, and the bit index reliabilitysequence to the polar encoder 215 for polar encoding.

In some examples, the transmitter sequence identifier 210 identifies abit index reliability sequence that is determined based on hybridpolarization weighting factors. The hybrid polarization weightingfactors may be applied using nested sequence generation. For example, afirst sequence may be generated for a given polar code length (e.g., N₁)using a first polarization weighting factor (e.g., β₁) and then a subsetof the sequence values may be replaced with a sequence of a secondlength (e.g., N₂, where N₂<N₁) that is generated using a secondpolarization weighting factor (e.g., β₂). The subset of the sequencevalues may correspond to the lowest (e.g., the lowest N₂) sequencevalues or the highest (e.g., the highest N₂) sequence values in thefirst sequence. Additional sequences may be nested using additionalpolarization weighting factors. Additionally or alternatively, hybridbit index weighting factors may be applied for a polarization weightfunction. For example, for a polar code having m bit positions (e.g.,where N=2^(m−1)), a first weighting factor may be applied for a firstsubset of the bit positions and a second weighting factor may be appliedfor a second subset of the bit positions.

In other examples, the transmitter sequence identifier 210 identifies abit index reliability sequence determined based on a UPO. Determiningthe bit index reliability sequence may involve an initial input searchsequence, which may also be known as an input sequence, containing allor a subset of the bit channel indices. The transmitter sequenceidentifier 210 may calculate the partial order under UPO of the inputsearch sequence and pick the most reliable bit-index under UPO. If thepicked bit-index is not the same order as another bit-index in the inputsearch sequence, it may be added to the bit index reliability sequence.Elsewise, analytical methods (e.g., index weighting by the Reed-Mullerrule), simulations, or both, which may select the index that maximizeslink-level performance, may be used to select the most reliablebit-index of that order, and that bit may be added to the bit indexreliability sequence. The selected bit may be removed from the inputsearch sequence and the method described above may be repeated until all(or a target number) of the input bit indices are selected. Parts of theresulting bit index reliability sequence may be modified using othersequences for index locations where those other sequences have betterperformance (e.g., by using the hybrid bit index weighting factorsdescribed above) as determined by simulations, estimated values,historical data, or some combination of these or other performancedetermining processes. It should be noted that the above method, in someexamples, may construct the bit index reliability sequence by pickingthe least reliable bit. It is also possible that the bits may be orderedby a single UPO property (e.g., property 1 as described below), whichmay result in violations of the other properties (e.g., violation ofproperty 2 arising as a result of the construction method).

FIG. 3 illustrates an example of diagram 300 of a polar code thatsupports information bit distribution design in accordance with variousaspects of the present disclosure. In some examples, diagram 300 mayimplement aspects of wireless communications system 100.

Diagram 300 depicts a polar code that includes N channels for generatinga polar-encoded codeword 320 with channel 0 illustrated on top, followedby channel 1, and proceeding sequentially to channel N−1. Channels u[0:N−1] 305 may represent bits to be encoded and codeword channels x[0:N−1] 325 may represent the bits once they are encoded. A generatormatrix 315 may be used (e.g., by multiplying the generator matrix 315 bychannels u[0: N−1] 305) by an encoder to encode information bits inputto the channels u[0: N−1] 305 to generate codeword channels x[0: N−1]325, and may be used (e.g., by multiplying codeword channels x[0: N−1]325 by the inversion of the generator matrix 315 or by another matrixderived from the generator matrix 315) by a decoder to decodeinformation received on codeword channels x[0: N−1] 325 to obtain arepresentation of the information bits and frozen bits on channels u[0:N−1] 305. The location of any particular channel may depend on itsreliability relative to other channels of the polar code.

The polar encoder 215, as discussed above with reference to FIG. 2, mayallocate the most reliable channels of a polar code to information bits(e.g., k information bits) and the least reliable channels of the polarcode to frozen bits (e.g., N−k frozen bits). The transmitter sequenceidentifier 210 may generate a bit index reliability sequence of length Nto inform the polar encoder 215 of the order in which to load bits intothe channels u[0: N−1] 305 (e.g., which k bit channels to select of theN bit channels of channels u[0: N−1] 305 for loading information bits).

FIG. 4 illustrates an example of a polar coding scheme 400 that supportsinformation bit distribution design in accordance with various aspectsof the present disclosure. In some examples, polar coding scheme 400 mayimplement aspects of wireless communications system 100.

In some cases, a transmitting device (e.g., a base station 105 or a UE115) may identify information for a transmission to a receiving deviceover a channel ‘W’ 405. In some examples, the polar coding scheme 400may be used to generate N=8 coded bits for the transmission from kinformation bits. As shown in polar coding scheme 400, an encodingprocess would proceed from left to right, while polarization may beunderstood as occurring in polarization stages proceeding from right toleft (e.g., bits transmitted over the channel ‘W’ 405 may be understoodas unpolarized, while bit channels 415 in the ‘U’ domain (e.g., ‘U’channels) are polarized bit channels having different reliability orcapacity). Polar coding scheme 400 may include a set of F and Goperations that are functions of logarithmic likelihood ratios (LLRs).In an example of a polar code LLR calculation:F(LLR_(a),LLR_(b))=Sign(LLR_(a))*Sign(LLR_(b))*min(|LLR_(a)|,|LLR_(b))G(LLR_(a),LLR_(b))=LLR_(b)+LLR_(a) if b=0G(LLR_(a),LLR_(b))=LLR_(b)−LLR_(a) if b=1

The transmitting device may locate the information bits on bit-channelinstances (or sub-channels) of the polar code associated with thehighest reliability (e.g., a higher place in a bit index reliabilitysequence). For instance, the bit index reliability sequence of the bitchannels 415 may be [7, 6, 5, 3, 4, 2, 1, 0] where N=8 and thereliability increases in ascending order. If there are 6 frozen bits and2 information bits, then the information bits may be loaded into channel111 (e.g., ‘U7’), which may be associated with the value 7, and channel110 (e.g., ‘U6’), which may be associated with the value 6, and thefrozen bits may be transmitted on the other channels, which may haveless reliability according to the bit index reliability sequence.

The bit-channel reliability may be determined according to apolarization weight that is associated with the number of repetitionoperations for a given bit-channel 415 and may represent a weightexperienced by the bit channel 415. The polarization weight maygenerally be given by:W _(i)=Σ_(j=0) ^(m−1) B _(j)·weight(j)where: i=binary(B_(m−1), B_(m−2), . . . B₀) and weight(j)=2^(j/4). B_(j)may be associated with the j^(th) bit of a bit representation of a bitchannel 415, where the bit representation may have m bits. For instance,bit channel ‘U5’ of FIG. 4 may have a bit representation of 101 and mmay be equal to 3. When i=5, then B₂ may equal 1, B₁ may equal 0, and B₀may equal 1. The weighting factor weight(j) may be understood asapplying a β factor, where β is given by the value of weight(1). Thus, βfor weight(j)=2^(j/4) may be equal to approximately 1.189 (e.g., if β isoptimized for a code length of N=4096, N=8192, etc.). However, a given βfactor optimized for a long code length (e.g., N=4096 or greater) maylimit performance when applied for shorter code lengths (e.g., N=64,128, etc.). As such, different functions may be used to define weight(j)for different code lengths. In this way, the β factor for a shorter codelength (e.g., β=1.17000 for N=512) may be different than the β factorfor a longer code length (e.g., β=1.189 for N=4096) if differentoptimizations for weight(j) are utilized.

The reliability may be determined according to a polarization weightwith hybrid polarization weighting factors. The hybrid polarizationweighting factors may be applied using nested sequence generation. Forexample, sequences may be generated using different beta values fordifferent sequence lengths N. In one example, a first sequence S₁ isgenerated for N=4096, 8192, using β₁=1.189, a second sequence S₂ isgenerated for N=1024, 2048 using β₂=1.17667, and a third sequence S₃ isgenerated for N=64, 128, 256, 512 using β₃=1.17000.

FIG. 5 illustrates an example of a polar code bit sequence generation500 that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, polar codebit sequence generation 500 may implement aspects of wirelesscommunications system 100. A first sequence 520 (e.g., with thereliability order of bit channels shown from top to bottom) may begenerated for a given polar code length (e.g., N_(x)=32) using a firstpolarization weighting factor (e.g., β_(x)=1.414). A subset of thesequence values may be replaced with a sequence 530 of a second length(e.g., N_(y)=16) that is generated using a second polarization weightingfactor (e.g., β_(y)=1.170). The polar code bit sequence generation 500may replace the bit locations within the first sequence 520corresponding to the lowest bit indices (e.g., 0-15) with the nestedsequence 530 to generate the final bit sequence 540. Although notillustrated, additional nesting may be performed using additional nestedsequences. In some examples, the highest bit indices (e.g., 16-31) maybe replaced instead of the lowest bit indices for a given nestingoperation. In some examples, a final sequence generated by nestingsequences generated with multiple polarization weighting factors may beused for multiple code lengths by using the order of the sequence valuesfor a given code length N. For example, a sequence of length N=8192generated using the nested sequence generation may be used for a codelength of N=128 by applying the order of the highest or lowestreliability bit channels (e.g., the order of bit channels 8191, 8190, .. . , 8064 or the order of bit channels 127, 126, . . . , 0) within theN=8192 sequence. In this way, one sequence may be used to determine bitorders for multiple different code lengths.

Additionally or alternatively, hybrid bit index weighting factors may beapplied for a polarization weight function. For example, for a polarcode having m bit positions (e.g., N=2^(m−1)) a first weighting factormay be applied for a first subset of the bit positions and a secondweighting factor may be applied for a second subset of the bitpositions.

Thus, weight(j) may be given by Π_(k=0) ^(j−1)(β(k))^(j/4). For example,where a polar code has length 4096 (e.g., m=12), β(k) may be given by β₁for k=11, β₂ for k=10, 9, and β₃ for k=8, . . . , 0, where β₁=1.189,β₂=1.17667, and β₃=1.17000.

FIG. 6 illustrates an example of Hasse diagram 600 that supportsinformation bit distribution design in accordance with various aspectsof the present disclosure. In some examples, Hasse diagram 600 mayimplement aspects of wireless communications system 100.

In some examples, with reference again to FIG. 2, the polar encoder 215may allocate the most reliable channels of a polar code to informationbits and the least reliable channels of the polar code to frozen bits.The transmitter sequence identifier 210 may generate a bit indexreliability sequence of length N to inform the polar encoder 215 of theorder in which to load bits into the channels. In an example, the bitindex reliability sequence of length N may specify reliability indescending order, and each bit index may correspond to a particularchannel.

Initially, the transmitter sequence identifier 210 may determine aninput search sequence that includes all or a subset of N bit indices [0,N−1]. The transmitter sequence identifier 210 may apply a UPO to aninput search sequence to obtain a partial order. The UPO may define apartial order on bit reliability based on one or more properties. Forexample, a first property of the UPO may dictate that a bit-index i hasthe same or higher reliability (e.g., under successive cancellationand/or maximum likelihood decoding) than a bit-index j if the binaryrepresentation of i has 1's at least in all the locations that the indexj has 1's. A second property may dictate that a bit-index i, generatedfrom a bit-index j by moving a 1 in the binary representation of j to amore significant location, has higher reliability than index j (e.g.,under successive cancellation decoding). In an example for N=8, i=3(011) is more reliable than i=2 (010) under Property 1, and i=4 (100) ismore reliable than i=2 (010) under Property 2. However, i=3 (011) andi=4 (100) are not comparable under either property.

Depicted in Hasse diagram 600 are a set of connected nodes 605, whereeach node 605 corresponds to a particular bit index. The values of thebit indices of the nodes 605 may correspond to an input search sequence.The Hasse diagram 600 may represent an ordering of the bit indices intoa bit index reliability sequence based on applying a UPO to an inputsearch sequence. Nodes 605 on the left (that is, where (0, 0, 0, 0) ison the far left and (1, 1, 1, 1) is on the far right) of the Hassediagram 600 may correspond to bit indices that are less reliable thanbit indices on the right. The bit index reliability may be determined byselecting the most reliable bit-index under the UPO. In the depictedHasse diagram, the bit index (1, 1, 1, 1) is the most reliable bitindex.

In some instances, the UPO may be unable to order some bit indicesrelative to others. For example, the UPO does not indicate a relativereliability of bit index (1, 1, 0, 0) and bit index (1, 0, 1, 1). As canbe seen, the Hasse diagram 600 depicts bit index (1, 1, 0, 0) in adifferent branch than bit index (1, 0, 1, 1). The Hasse diagram 600depicts other instances of bit indices that are not ordered relative toone another, such as bit index (1, 0, 0, 0) and bit index (0, 0, 1, 1).Such indices may be considered to have a same order under the UPO (e.g.,these bit indices may be treated as equally reliable or approximatelyequally reliable under the UPO).

If the UPO does not identify a single bit index as being more reliablethan another, the techniques described herein may be applied forselecting between at least two indices having a same order under theUPO. In one example, an analytical method may be applied to the partialorder to obtain calculated relative orders of bit indices not ordered inthe partial order. Dashed line 610-a may represent a situation where theUPO does not provide an order between bit index (1, 1, 0, 0) and bitindex (1, 0, 1, 1), so these indices may not be ordered relative to oneanother in the partial order. Dashed line 610-b is another example wherethe UPO may not provide an order between bit index (1, 0, 1, 0) and bitindex (0, 1, 1, 1) that are not ordered relative to one another in thepartial order.

An analytical method may be applied to obtain calculated relative ordersof bit indices not ordered in the partial order. For example, theanalytical method may include applying a Reed-Muller rule, an indexpolarization weight rule, a density evolution (DE) rule, a mutualinformation-DE (MI-DE) rule, or any combination thereof, for selectingwhich of the at least two indices (e.g., bit indices (1, 1, 0, 0) and(1, 0, 1, 1)) is the most reliable. In some cases, the analytical methodmay be utilized to determine relative reliabilities for more than twobit indices (e.g., for a Hasse diagram 600 with more than two branches).

In some examples, the calculated relative orders of the at least two bitindices may violate at least one of the first property or the secondproperty of the UPO. In some examples, satisfying property 1 of the UPOmay lead to a better sequence (e.g., more reliable than using anabsolute order rule alone), but violating property 2 may sometimesimprove the performance under list decoding, maximum-likelihooddecoding, or the like. In some instances, the property 2 violation mayoccur as a result of a construction method such as some versions ofMI-DE. For example, only a single property (e.g., property 1) of the UPOmay be applied to an input search sequence to generate a partial order,and an analytical method may be used to evaluate reliabilityrelationships between bit indices not ordered (or of seemingly equalorder) in the partial order. The analytical method may be applied toobtain calculated relative orders of bit indices not ordered in thepartial order. In some examples, the calculated relative orders of theat least two bit indices may violate at least one property of the UPO(e.g., the calculated relative orders may violate property 2). A bitindex reliability sequence generated in such a manner may thus includeat least some bit indices placed in an order in the reliability sequencethat violates a property of the UPO. Alternatively, both properties ofthe UPO may be applied to the input search sequence to generate thepartial order, and selected bit indices may be rearranged based onresults of an analytical method (e.g., where an analytical method showsa large benefit to rearranging bit indices).

In some examples, a simulation may be applied to refine an order of theat least two bit indices selected based on the calculated relativeorders. For example, link-level performance simulation may be used forselecting which of the at least two indices is more reliable (e.g., theindex with higher link-level performance may be chosen). In someexamples, the simulation may be based on a list size applied by asuccessive cancellation list decoding algorithm for decoding thecodeword. In an example, the analytical method may determine areliability for each bit index not ordered in the partial order. Whencomparing two bit indices, the analytical method may determine adifference in the reliabilities for the two bit indices. If thedifference satisfies a threshold (e.g., is greater than or equal to thereliability difference threshold), the two bit indices may be added tothe bit index reliability sequence in an order corresponding to thedetermined reliabilities. In some examples, one of the two bit indices(e.g., the more reliable bit index) may be added to the bit reliabilitysequence and the other may remain in an input search sequence. If,however, the difference does not satisfy the threshold (e.g., is lessthan the threshold), simulation may be used to determine the relativeorders between the two bit indices in the bit index reliabilitysequence. Thus, the subset of bit indices for which the partial orderdoes not resolve bit index ordering may be further reduced using theanalytical method, with bit indices having similar bit reliabilities asgiven by the analytical method being simulated to determine theperformance difference between different orderings for the bit indices.In this manner, simulation time may be reduced by simulating only thosebit-channel index order pairs for which the UPO and analytical methodsdo not indicate a strong preference (e.g., based on reliability) in thebit-channel index order.

Once a particular bit index from the input search space (i.e., the inputsearch sequence) pace is added to the reliability sequence, theparticular bit index may be removed from the input search space. Theprocess may be repeated to generate a bit sequence reliability order fora desired length of N. Based on the description above, to generate areliability sequence of length N (in descending reliability order), aninput search sequence may be to all or a subset of the bit indices in[0, N−1], and a partial order under UPO of the input search sequence maybe calculated. The most reliable bit-index under UPO may be selected. Ifmultiple bit indices under the UPO have a same order, select from amongthe multiple bit indices using an index selection criterion. The indexselection criterion may be another analytical method to select from thebit indices or selecting the bit index that maximizes link-levelperformance via simulation. The selected bit index may be added to theoutput bit index reliability sequence, and may be removed from the inputsearch sequence to generate an input search subsequence. The process maybe repeated using the input search subsequence until all (or a targetnumber) of the input bit indices are selected for the bit indexreliability sequence.

The following are example bit index reliability sequences determined forN=128, N=256, and N=512 using the techniques described above.

N=128 Sequence:

[127, 126, 125, 123, 119, 111, 124, 95, 122, 121, 118, 63, 117, 110,115, 109, 94, 107, 93, 62, 103, 120, 91, 116, 61, 87, 114, 59, 108, 79,113, 55, 106, 92, 47, 105, 102, 31, 90, 101, 89, 60, 86, 99, 58, 85, 78,112, 57, 54, 83, 77, 104, 53, 46, 75, 100, 51, 45, 71, 88, 30, 98, 43,84, 29, 97, 39, 27, 56, 82, 76, 23, 52, 15, 81, 74, 44, 50, 73, 70, 42,49, 69, 28, 96, 41, 67, 38, 26, 37, 25, 22, 80, 35, 21, 72, 14, 48, 19,13, 68, 40, 11, 7, 66, 36, 24, 65, 34, 20, 33, 18, 12, 17, 10, 9, 6, 64,5, 3, 32, 16, 8, 4, 2, 1, 0]

N=256 Sequence:

[255, 254, 253, 251, 247, 239, 252, 223, 250, 249, 246, 191, 245, 238,243, 237, 127, 222, 235, 221, 248, 190, 231, 219, 244, 189, 215, 242,126, 187, 236, 207, 241, 125, 234, 183, 220, 233, 123, 230, 175, 218,229, 119, 159, 214, 217, 111, 188, 227, 186, 213, 95, 206, 240, 185,211, 182, 124, 205, 203, 232, 181, 63, 174, 122, 228, 179, 199, 121,173, 216, 158, 118, 226, 117, 171, 212, 110, 157, 225, 115, 167, 184,204, 109, 155, 210, 94, 180, 107, 151, 209, 202, 93, 143, 178, 62, 172,103, 201, 61, 198, 120, 177, 91, 170, 197, 87, 116, 156, 195, 114, 169,79, 59, 166, 224, 108, 154, 113, 165, 55, 153, 106, 208, 150, 92, 163,47, 102, 149, 200, 105, 90, 142, 31, 101, 176, 147, 89, 141, 196, 86,60, 99, 139, 168, 85, 58, 194, 78, 135, 57, 164, 83, 112, 54, 77, 152,193, 46, 53, 162, 104, 75, 148, 51, 100, 71, 45, 161, 30, 146, 140, 88,43, 98, 29, 145, 138, 84, 39, 97, 27, 137, 82, 56, 76, 23, 134, 192,133, 52, 15, 81, 74, 50, 44, 131, 73, 70, 160, 42, 49, 69, 28, 144, 41,67, 26, 38, 96, 136, 37, 25, 22, 132, 35, 80, 21, 14, 72, 130, 19, 13,48, 68, 11, 129, 40, 7, 66, 36, 24, 65, 34, 20, 33, 18, 12, 17, 10, 128,6, 9, 5, 64, 3, 32, 16, 8, 4, 2, 1, 0]

A portion (e.g., the bit indices with the higher reliabilities) of theN=512 Sequence:

[511, 510, 509, 507, 503, 495, 508, 479, 506, 505, 502, 447, 501, 494,499, 493, 383, 478, 491, 477, 504, 487, 475, 446, 500, 255, 445, 471,498, 492, 443, 497, 382, 463, 490, 439, 381, 476, 489, 486, 379, 474,431, 485, 473, 254, 444, 375, 470, 483, 253, 415, 442, 469, 496, 367,462, 251, 441, 467, 438, 380, 461, 247, 351, 488, 430, 459, 239, 437,378, 319, 435, 484, 223, 429, 455, 377, 472, 374, 414, 482, 252, 427,373, 191, 468, 366, 413, 466, 423, 250, 481, 371, 440, 365, 411, 460,249, 350, 246, 436, 407, 349, 458, 465, 363, 238, 399, 127, 434, 428,245, 359, 454, 318, 457, 376, 347, 243, 433, 237, 426, 453, 222, 343,372, 412, 317, 235, 425, 451, 370, 315, 422, 221, 480, 364, 335, 410,231, 190, 369, 421, 311, 409, 219, 248, 464, 362, 406, 348, 419, 189,244, 303, 358, 215, 405, 456, 361, 398, 126, 242, 346, 187, 236, 403,357, 316, 432, 207, 287, 397, 452, 342, 125, 345, 234, 241, 123, 355,395, 424, 183, 314, 341, 220, 450, 233, 391, 334, 230, 420, 175, 313,218, 119, 339, 368, 310, 408, 229, 333, 449, 214, 159, 217, 309, 360,331, 418, 188, 227, 302, 404, 111, 213, 307]

In the N=512 sequence, in some examples, fewer than 201 information bitsmay be included, and the portion of the bit index reliability sequenceshown above may correspond to the payload range of interest, and therest of the bit index reliability sequence may be constructed usinganother method.

The proposed techniques can may be altered to generate the bit indexreliability sequence in ascending order. Moreover, in some examples,portions of the resulting bit index reliability sequence may be modifiedusing at least one other sequence at selected index locations wherethose sequences are determined to have better performance.

With reference to FIG. 2, the polar encoder 215 may generate a codewordof length N based on the bit index reliability sequence and a set of kinformation bits received from the data source 205. With reference toFIG. 3, the k information bits may be loaded into the most reliablechannels determined from the bit index reliability sequence, and theencoder may apply a generator matrix 315 to the input information bitsand frozen bits (e.g., channels u[0: N−1] 305) in order to output acodeword 320. The polar encoder 215 may pass the encoded bits of thecodeword 320 to a rate-matcher (not shown) to rate-match the encodedbits to a set of resources for the transmission to a receiving device(e.g., a UE 115). When rate-matching is employed, a subset of the N bitsmay be transmitted or a subset of the N bits may be repeated in thetransmission. In some examples, channel reliability is computed for eachM: N: K combination, where M is the number of the N bits of the codeword320 that are transmitted, and M may be less than (puncturing) or greaterthan (repetition) N. The rate matcher may then input the rate-matchedbits to a modulator (not shown) for modulation prior to the transmission(e.g., to UE 115-a). The transmitting device (e.g., base station 105-a)may then transmit the rate-matched codeword to the receiving device(e.g., UE 115-a) over communication channel 235.

UE 115-a may identify a candidate codeword based on a candidatehypothesis (e.g., decoded resources, one or more M: N: K hypotheses,etc.). For example, UE 115-a may employ a blind decoding process inwhich multiple candidate hypotheses within a search space are tested todetermine if a successful decoding is performed for any of the candidatehypotheses. Demodulator 220 may demodulate the candidate codeword, whichmay include demapping received symbols associated with a set ofresources to obtain a representation of the codeword 320. Demodulator220 may then pass the representation of the codeword to a receiversequence identifier 225. The receiver sequence identifier 225 maydetermine a length of the codeword 320 and may select a bit indexreliability sequence corresponding to the determined length. Thereceiver sequence identifier 225 may output the bit index reliabilitysequence and the representation of the codeword to decoder 230 toidentify the most likely candidate path or paths for the informationbits obtained from the codeword. The demodulated signal may be, forexample, a sequence of logarithmic-likelihood ratio (LLR) valuesrepresenting a probability value of a received bit being a ‘0’ or a ‘1.’The decoder may perform a list decoding algorithm on the LLR values(e.g., successive cancellation list decoding, maximum likelihooddecoding) and may provide an output. If the decoder is able to decodethe codeword successfully, the decoder may output a bit sequence of theinformation vector (e.g., the k information bits) for use, storage,communication to another device, or the like.

Advantageously, the techniques described herein may merge benefits fromdifferent construction methods and identify channels having improvedlink-level performance. In some examples, an absolute order rule may befollowed, and a UPO rule may be selectively applied. Beneficially, theexamples described herein may provide techniques for identifying areliability order for channels of a polar code.

The techniques described herein may further improve bit allocation at aquantization boundary. Bit channels of a polar code may be recursivelypartitioned at one or more polarization stages of the polar code using abaseline rate allocation rule. The baseline rate allocation rule mayhave ceiling and floor operations that control the allocation of bits atquantization boundaries (e.g., because of the allocation of integernumbers of information bits to each partition). One or more quantizationrules may be applied for determining whether to assign a number of bitsof a bit channel partition to a fixed value. In some examples, assigninginformation bits to a partition may be adjusted to be compliant with aUPO.

FIG. 7 illustrates an example of a wireless communications device 700that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, device 700may implement aspects of wireless communications system 100. In somecases, device 700 may be a UE 115 or a base station 105 as describedwith reference to FIG. 1.

Device 700 may include memory 705, encoder/decoder 710, andtransmitter/receiver 715. Bus 720 may connect memory 705 andencoder/decoder 710, and bus 725 may connect encoder/decoder 710 andtransmitter/receiver 715. In some instances, device 700 may have datastored in memory 705 to be transmitted to another device, such as, a UE115 or a base station 105. To initiate data transmission, device 700 mayretrieve the data, including information bits, from memory 705 for thetransmission. The k information bits included in memory 705 may bepassed on to encoder/decoder 710 via bus 720. After the information bitsare encoded (e.g., along with a set of N−k frozen bits), a resultingcodeword, which may have a length N or greater (e.g., when containingparity bits), may be passed on to transmitter/receiver 715 via bus 725.The number of information bits may be represented as a value k, asshown.

Encoder/decoder 710, acting as an encoder, may encode the k informationbits and output a codeword having a length N, where k<N. Parity bits maybe used in some forms of outer codes to provide redundancy to protectinformation bits, and frozen bits may be denoted by a given value (0, 1,etc.) known to both the encoder and the decoder (i.e., the encoderencoding information bits at a transmitter of a first device 700, andthe decoder decoding the codeword received at a receiver of a separatedevice 700). From a transmitting device perspective, device 700 mayencode information bits to produce a codeword, and the codeword may betransmitted via transmitter 715. From a receiving device perspective,device 700 may receive encoded data (e.g., a codeword) via receiver 715and may decode the encoded data using decoder 710 to obtain theinformation bits.

Device 700 may generate a codeword of length N and dimensionality k(e.g., corresponding to the number of information bits) using a polarcode. A polar code is an example of a linear block error correcting codethat has been shown to approach channel capacity as the block length Nincreases. Implementing polar codes may increase the probability of asuccessful transmission. During encoding, a set of unpolarized bitchannels may be transformed into polarized bit channels (e.g., channelinstances or sub-channels) that may each be associated with areliability metric. A reliability metric of a polarized bit channel mayapproximate the ability of the polarized bit channel to successfullyconvey an information bit to a receiver. Each polarized bit channel maythen be loaded with an information bit or non-information bit (e.g., afrozen bit, parity bit, etc.) for a transmission based on thereliability metrics of different polarized bit channels.

In some cases, reliability metrics may be determined based on arecursive partitioning of bit locations (e.g., channel instances orsub-channels) of the polar code. In a first polarization stage, a set ofunpolarized bit channels may be polarized, and the resulting polarizedbit channels may each be associated with a reliability metric determinedbased on the reliability metric (or mutual information (MI)) of theunpolarized bit channels. The polarized bit channels may then bepartitioned into sectors or groups based on the determined reliabilitymetrics of the different polarized bit channels. For example, the bitchannels corresponding to the single parity check operation may bepartitioned into a first, lower reliability group, while the bitchannels corresponding to a repetition operation may be partitioned intoa second, higher reliability group. The polarization process maycontinue recursively until each partition reaches a given size.

A device 700 may identify a number of information bits (e.g., of aninformation bit vector) for transmission, and the transmitting devicemay allocate or distribute the information bits to different groups ofpolarized bit channels during the recursive partitioning based on acapacity of the different groups. Since the capacity of the differentgroups may be based on the reliability metric of different polarized bitchannels, subsets of the information bits may be distributed orallocated to different groups of polarized channels based on thereliability metrics associated with the different groups of polarizedchannels. The information bits may then be assigned to specificpolarized bit channels within a group based on a polarization metric(e.g., a polarization weight, a density evolution (DE), etc.). Assigninginformation bits within each group may be based on a predeterminedranking of bit channels within the groups. As such, the information bitsmay be loaded on the polarized bit channels associated with the highestreliability metrics, and the remaining bits (e.g., parity bits, frozenbits, or both) may be loaded on the remaining polarized bit channels.

In some cases, however, the capacity of the unpolarized bit channels maynot be the same (e.g., due to puncturing). In such cases, if a polarcode does not account for punctured bits, the information bits may notbe allocated or distributed to the most favorable bit locations (i.e.,bit locations associated with the highest reliability). Accordingly, awireless device may experience reduced throughput. Device 700 maysupport efficient techniques for facilitating puncturing in a polarcoding scheme. Specifically, the recursive partitioning of bit channelsinto polarized bit channels may be based on the overall capacity for atransmission adjusted based on the number of bits punctured. Thecapacity of different sectors and groups of polarized bit channels maythus be altered according to the adjusted polarized bit capacity, and adevice may be able to allocate or distribute information bits to themost favorable bit locations.

In some examples, the device 700 may map coded bits of a polar code todifferent groups of bit channels of a certain size ‘S’ (e.g., 64 bitchannels at a third stage of polarization 805-c, as described below withreference to FIG. 8).

FIG. 8 illustrates an example of a polar code construction scheme 800that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, polar codeconstruction scheme 800 may be implemented by aspects of wirelesscommunications system 100 (e.g., a UE 115, base station 105, etc.).

The depicted example is a fractally enhanced kernel (FRANK) polar codeconstruction scheme, which is an iterative polar code constructionscheme. The recursion in the iterative polar code construction schememay be terminated when a specific block size is reached (e.g., a blocksize equal to or smaller than a certain block size threshold). Forexample, if the size of a nested polar code is equal to N_(t), then oneor more pre-calculated sequences of length N_(t) may be used todetermine an allocation of information bits within each nested polarcode. The one or more pre-calculated sequences may be derived using, forexample, polarization-weight techniques, DE techniques, MI techniques,or the like. For example, the pre-calculated sequence may be an exampleof a bit index reliability sequence described with respect to FIG. 6.

The coded bits may be mapped to bit channels in a group using a fixedsequence that is based on a polarization metric (e.g., polarizationweight, DE, etc.). The fixed sequence may be described using S*log₂ Sbits, where ‘S’ corresponds to the number of bit channels. Additionally,the group that includes each coded bit of the polar code may bedescribed using

${\log_{2}\frac{N}{S}{bits}},$and the groups that include all bits of the polar code may be describedusing

$N*\log_{2}\frac{N}{S}{{bits}.}$Thus, the number of bits used to describe the bit locations of all bitsin the polar code may be equal to

${S*\log_{2}S} + {N*\log_{2}\frac{N}{S}{{bits}.}}$This may use fewer bits than in the case of using an explicit orderingof bit channels.

As described herein, the bit locations for information bits for a polarcode used to encode a codeword to be transmitted or used to decode areceived codeword may be efficiently described using recursivepartitioning and binary partition assignment vectors. Specifically, bitchannels for one or more stages of polarization may be recursivelypartitioned, and the information bits for each stage of polarization maybe assigned to sub-partitions based on a binary partition assignmentvector. Each bit of the binary partition assignment vector may determinethat an information bit, if present for the partition, is assigned to afirst sub-partition (e.g., a higher reliability partition) or a secondsub-partition (e.g., a lower reliability partition). As an example, foran information bit of the K information bits in FIG. 8, the wirelessdevice may determine that a binary partition assignment vector at stage805-a indicates that the information bit is loaded onto a bit channel ina lower group of bit channels (K₁). The wireless device may thenpartition the bit channels of the K₁ information bits—including theinformation bit—and determine that a binary partition assignment vectorat stage 805-b indicates that the information bit is loaded onto a bitchannel in a lower group of bit channels (K₁₁).

At the third stage of polarization 805-c, the recursive partitioning ofbit channels may terminate if each group of bit channels at the thirdstage of polarization 805-c includes a certain number of bit channels‘S’ (e.g., a number of bit channels that is less than or equal to athreshold number of bit channels). The number of information bits thathave propagated to each group may then be assigned to a specific bitchannel of the group based on a fixed sequence. Using these techniques,the bit locations of each coded bit of a polar code may be describedusing N bits at stage 805-a and N/2 bits at stage 805-b. Then, at stage805-c, the bit locations of each coded bit may be based on the fixedsequence which may be described using S*log₂ S bits. Thus, the number ofbits used to describe the bit locations of all bits in the polar codemay be equal to S*log₂ S+N+N/2 bits, which may be less than the numberof bits used to describe the bit locations of all bits in the polar codeusing the other conventional techniques described above. The techniquecan be extended as additional stages are present in the polar code tosupport higher values of N. The number of bits used for any given valueof N may be given by S*log₂ S plus the sequence

${N + \frac{N}{2} + {\frac{N}{4}\mspace{14mu}\ldots} + {2S}},$which approaches the limit of 2N as N increases. Thus, the upper boundfor describing the locations for information bits of the polar codehaving any of multiple code lengths satisfying 2^(m), where m is aninteger, up to and including N, may be given by S*log₂ S+2N.

FIG. 9 illustrates an example of a polar code construction scheme 900that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, polar codeconstruction scheme 900 may implement aspects of wireless communicationssystem 100. The depicted example may provide a reduced descriptioncomplexity scheme for constructing a polar code. Short sequence(s) maybe used in the iterative polar code construction scheme of FIG. 8. Foreach information bit, an indication may be used to indicate which smallsequence it is mapped to. The mapping may indicate whether each bit ismapped to the more reliable sequence(s) or less reliable sequence(s). Inthe depicted example, log(N/S) bits may be used for each increment of K.

As illustrated, in one specific example, if K=1, the one information bitmay be mapped to the K₁₁ partition (e.g., the K₁₁ group of bitchannels). Similarly, if K=2, the two information bits may be mapped tothe K₁₁ partition. However, if K=3, two of the three information bitsmay be mapped to the K₁₁ partition, and one of the three informationbits may be mapped to the K₁₀ partition. Which information bit is mappedto which of the allocated partitions may be based on priority values ofthe information bits, an order of the information bits in theinformation bit vector, or any other procedure for splitting the bitsbetween the partitions. It is to be understood that further bitallocations may be defined for larger values of K, larger numbers ofpartitions, etc.

FIG. 10 illustrates an example of a polar code construction scheme 1000that supports information bit distribution design in accordance withvarious aspects of the present disclosure. In some examples, aspects ofwireless communications system 100 (e.g., UEs 115, base stations 105,etc.) may implement polar code construction scheme 1000.

Depicted on the right in an initial stage is an unpolarized bit sequencehaving K information bits 1005 and N total bits (e.g., information andfrozen bits). The polar code construction scheme 1000 may partition theK information bits at first and second polarization stages. At the firstpolarization stage, K₀ of the K information bits may be allocated topartition 1015-a, and K₁ of the K information bits may be allocated topartition 1015-b. At the second polarization stage, K₀₀ of the K₀information bits may be allocated to partition 1025-a, and K₀₁ of the K₀information bits may be allocated to partition 1025-b. Also at thesecond polarization stage, K₁₀ of the K₁ information bits may beallocated to partition 1025-c, and K₁₁ of the K₁ information bits may beallocated to partition 1025-d. It should be understood that thetechniques described herein may be applied to additional polarizationstages than those illustrated in FIG. 10.

In a sequence based polar code description, a collective sum MI of W_(i)⁺ and W_(i) ⁻ channels at a particular polarization stage may be definedas R_(i) ⁺ and R_(i) ⁻ respectively, where R_(i) ⁺ and R_(i) ⁻ arederived from the MI of channel W_(i). Recursion using the followingbaseline rate allocation rule may be used for allocating informationbits:

$K_{i}^{+} = \left\{ {\begin{matrix}{\left\lceil {R_{i}^{+} \times {N_{i}/2}} \right\rceil,} & {{{when}\mspace{14mu} K_{i}} \leq {0.5N_{i}}} \\{\left\lfloor {R_{i}^{+} \times {N_{i}/2}} \right\rfloor,} & {{{when}\mspace{14mu} K_{i}} > {0.5N_{i}}}\end{matrix},} \right.$where i identifies a particular partition in a particular polarizationstage, K_(i) represents the number of information bits at partition i,and N_(i) represents the total number of bits of partition i. It shouldbe noted that the “┌ ┐” symbol represents a ceiling operation and the “└┘” symbol represents a floor operation.

The total number of bits of a partition may decrease by half at eachpolarization stage. In such a case, the total number of bits at theinitial stage is N bits, the total number of bits for each partition(e.g., partitions K₀, K₁) at the first polarization stage is N/2 bits,the total number of bits for each partition (e.g., partitions K₀₀, K₀₁,K₁₀, K₁₁) at the second polarization stage is N/4 bits, and so forth. Asshown in FIG. 10, the number of information bits K₁ at partition 1015-bmay be determined using the above equation based on the number ofinformation bits K at the initial stage and the total number ofinformation bits at the partition (e.g., N₁=N/2 bits). Similarly, thenumber of information bits K₁₁ at partition 1025-d may be determinedusing the above equation based on the number of information bits K₁ andthe total number of information bits at partition 1025-d (e.g., N₁₁=N₁/2bits=N/4 bits). Also, the number of information bits K₀₁ at partition1025-b may be determined using the above equation based on the number ofnumber of information bits K₀ and the total number of information bitsat partition 1025-b (e.g., N₀₁=N₀/2 bits=N/4 bits). It follows that thenumber of information bits K₀₀ at partition 1025-a may be determinedbased on the output of the above equation, as K₀ ⁻=K₀−K₀ ⁺.

For an additive white Gaussian noise (AWGN) channel, the relationshipbetween R_(i) ⁺, R_(i) ⁻ and R_(i) may be defined as:C _(awgn) ⁺=2C−C ²−α and C _(awgn) ⁻ =C ²+α,where

${\alpha = {{- \frac{{C - 0.5}}{32}} + \frac{1}{64}}},$or α=0.

It should be noted that R_(i) ⁺ may correspond to or may be put into theabove equations as the value of C_(awgn) ⁺, R_(i) ⁻ may correspond to ormay be put into the above equations as the value of C_(awgn) ⁻, andR_(i) may correspond to or may be put into the above equations as thevalue of C.

The above equation for determining K_(i) ⁺ may provide symmetric orsubstantially symmetric allocation of information bits and frozen bitsto each partition. In some situations, introducing asymmetry may improveperformance of the polar code, such as at a quantization boundary wheresymmetry may not be necessary or may be undesirable. A quantizationboundary may occur where a bit could be allocated either to a W⁻ or W⁺channel. Conventionally, low rate information bit allocation has beenconsidered a dual of high rate frozen bit allocation. Thus,conventionally there has been a symmetric relationship betweenallocation of frozen bits and information bits. Information bits areconsidered to have a low rate (e.g., a low coding rate) when frozen bitshave a high rate, and information bits are considered to have a highrate when frozen bits have a low rate. However, this may not always bethe case. For low rate information bit allocation, the techniquesdescribed herein generally allocate an information bit to W⁺ to be moreconservative because over-allocating information bits to W⁻ may causelarge degradation and conservative K⁻ allocation of information bits maybe desirable. In some examples, up to all frozen bits may be allocatedto W⁻. For a low coding rate, it may be in general better to allocateinformation bit(s) to W⁺ to be more conservative.

For high rate information bit allocation, the techniques describedherein may allocate a frozen bit to W⁺ to be more conservative becauseover-allocation of information bits to W⁺ may cause large degradationand conservative K⁺ allocation of information bits may be desirable. Insome examples, allocation of up to all frozen bits to W⁻ may bepreferred. At the quantization boundary, symmetry may not hold anddifferent quantization rules described below may be used to break thesymmetry.

The examples described herein may provide one or more quantization rulesto introduce asymmetry based on the baseline rate allocation rule. Inthe baseline rate allocation rule, the “┌ ┐” symbol represents a ceilingoperation and the “└ ┘” symbol represents a floor operation. As aresult, at the quantization boundary, the number of information bitsK_(i) ⁺ may approach N_(i)/2 as R_(i) approaches 1, but K_(i) ⁺ maynever reach N_(i)/2 under the baseline rate allocation rule. Tointroduce asymmetry, one or more quantization rules may be used fordetermining when to set the number of information bits K_(i) ⁺ to afixed value. In some cases, the fixed value is a function of a number ofbit channels of the partition and may be equal to the number of bitchannels of the partition (e.g., N_(i)/2).

Below are examples of Rule 1 and Rule 2 of information bit allocation(asymmetric) quantization rules:

Rule 1:K _(i) ⁺ =N _(i)/2, when (1−R _(i) ⁺)×N _(i)/2≤Δ,where, in one example,

$\Delta = {\frac{1}{32} + {\frac{1}{16}.}}$In a second example,

${\Delta = \frac{1}{16}},$or it may be equal to other values (e.g., the value of Δ, in some cases,may depend on N_(i)).

Rule 2:

${K_{i}^{+} = \frac{N_{i}}{2}},{{{when}\mspace{14mu} K_{i}} \geq {N_{i} - {\log_{2}\left( N_{i} \right)} + \delta}},$where δ=0, or δ may be a correction term (e.g., the value of δ maydepend on N_(i)). In some examples, the values for Δ, δ, or both may beselected to generally ensure or enforce a UPO.

Rule 1 may be used to set the number of information bits K_(i) ⁺ to afixed value when the collective capacity R_(i) ⁺ approaches 1 such thata corresponding difference (e.g., a difference between the collectivecapacity R_(i) ⁺ when multiplied by the total number of information bitsin the partition and the total number of information bits in thepartition K_(i) ⁺) is less than or equal to a threshold. The thresholdmay be dependent on the number of bit channels of the partition and/ormay be selected to maintain a UPO of the bit channels of the partition.

Rule 2 may be used to set the number of information bits K_(i) ⁺ to afixed value when the calculated number of information bits K_(i) exceedsa difference between the total number of bits N_(i) of a partition andlog₂(N_(i)). Rule 2 may be a function of a code rate of the partitionand/or may be selected to maintain a UPO of the bit channels of thepartition.

The baseline rate allocation rule above may not indicate the number ofinformation bits K_(i) ⁻, which may be determined as a function of K_(i)⁺ by subtracting K_(i) from K_(i) ⁺ (e.g., according to K_(i)⁻=K_(i)−K_(i) ⁺). The baseline rate allocation rule and one or more ofthe quantization rules may be recursively applied to determine thenumber of information bits K for each partition in the polar codeconstruction scheme 1000. For example, either one or the otherquantization rule may be applied or some combination of the rules may beapplied, and the number of information bits K_(i) ⁺ may be set to thefixed value if either rule is satisfied.

The examples provided herein may be utilized with other baseline rateallocation rules. For example, the baseline rate allocation ruledescribed above may be generalized when MI of a set of bits isdetermined to be reliable (e.g., if the capacity exceeds a threshold).In this case, the set of bits may be allocated with R=1, whileotherwise, bits may be allocated to other blocks (i.e., sets of bits).

When accumulative MI, R, is close enough (e.g., less than a thresholddifference) to the number of coded bits, K_(i) ⁺ and K_(i) ⁻ may bedirectly saturated to the corresponding number of unpunctured codedbits, where the number of unpunctured coded bits of W_(i) ⁺ and W_(i) ⁻may be defined as M_(i) ⁺ and M_(i) ⁻ using the following equations:

$K_{i}^{+} = \left\{ {\begin{matrix}{M_{i}^{+},{{{{when}\mspace{14mu} M_{i}^{+}} - I_{i}^{+}} \leq \Delta}} \\{{K - M_{i}^{-}},{{{{when}\mspace{14mu} M_{i}^{+}} - I_{i}^{+}} \leq \Delta},{{M_{i}^{+} - I_{i}^{+}} > \Delta}}\end{matrix},{\Delta = {\frac{1}{32} + \frac{1}{16}}},} \right.$Like above, K_(i) ⁻ may be obtained by subtracting K_(i) from K_(i) ⁺,such that K_(i) ⁻=K_(i)−K_(i) ⁺.

These techniques may be used for determining the number of informationbits allocated to partitions at each polarization stage shown in FIG.10, and the techniques may be extended to any desired number ofpolarization stages.

With reference again to FIG. 7, the wireless communications system 700may implement these techniques. The following describes a base station105 encoding a codeword using these techniques for transmission to a UE115 and the UE 115 receiving and decoding the codeword. The roles may bereversed, and the UE 115 may encode a codeword using these techniquesfor transmission to the base station 105, with the base station 105receiving and decoding the codeword.

In an example, an encoder 710 of transmitting device (e.g., a basestation 105) may encode a codeword using a polar code for a transmissionover a wireless channel, where the codeword includes an information bitvector including multiple information bits. The encoder 710 may identifya set of bit locations of a polar code for a set of information bits,where the set of bit locations is determined based on a recursivepartitioning of multiple bit channels of the polar code for at least asubset of polarization stages of the polar code, as described in FIGS. 8and 10. The encoder 710 may, for each partition of at least the subsetof the polarization stages of the polar code, assign portions of anumber of the information bits of each partition to bit channelsub-partitions. The encoder 710 may apply at least one quantizationrule, such as Rule 1 and/or Rule 2, for determining whether to assign afirst number of the information bits of a first bit channelsub-partition of the bit channel sub-partitions to a fixed value. Insome cases, encoder 710 may, for a particular partition, assign a numberof information bits of the particular partition based on the baselineallocation rule. In some examples, the encoder 710 may assign portionsof a number of the information bits of each partition to bit channelsub-partitions by adjusting the information bit allocation derived basedon the recursive partitioning to be compliant with a UPO. The encoder710 may adjust the information bit allocation by constructing a sequencefor a partition that is compliant with the UPO, generate a bit vectorfor assigning the number of the information bits according to an MIrecursion equation, and compare an order resulting from the bit vectorto the UPO. In some examples, the encoder 710 may determine, for a valueof the bit vector for the partition, that the order resulting from thevalue of the bit vector violates the UPO and may swap the value of thebit vector with an adjacent value of the bit vector based on identifyingthat the value violates the UPO. In some examples, encoder 710 maydetermine the sequence is determined based on a binary bit weightingthat applies multiple weighting factors for the bit channels of thepartition, similar to that described above in FIG. 4. The encoder 710may provide the codeword encoded according to the polar code based onthe set of bit locations to the transmitter 715. The transmitter 715 ofthe transmitting device may transmit the encoded codeword over thewireless channel.

At a receiving device (e.g., a UE 115), a receiver 715 may receive theencoded codeword, and a decoder 715 may identify the set of bitlocations of the polar code for the set of information bits using asimilar process to that described above for the encoder 710. The decoder710 may decode the received codeword according to the polar code toobtain an information bit vector at the set of bit locations. The UE 115and the base station 105 may, in some examples, exchange a table thatincludes different sets of bit locations, and may exchange controlinformation that includes an index indicating which set of bit locationsto use for encoding and decoding of a codeword. In some cases, thedevices may be pre-configured with a table (e.g., a lookup table), wherethe table is generated using one or more of the techniques describedabove. An encoding device and a decoding device may each use a lookuptable stored in memory to determine bit indices for information bits(e.g., where the values in the lookup table are based on thequantization rules as described above).

In some instances, the baseline allocation rules or quantization rulesmay result in an allocation of information bits that may violate UPO. Anadditional bit-reordering step may be applied to provide a UPO compliantpolar code information allocation.

FIG. 11 illustrates an example of diagram 1100 of bit sequencereordering that supports information bit distribution design inaccordance with various aspects of the present disclosure. In someexamples, bit sequence reordering diagram 1100 may correspond toprocesses or functions performed by aspects of wireless communicationssystem 100 (e.g., base stations 105 or UEs 115).

For a large value of N, information bits may be distributed by updatingthe sequence information allocation and quantization of corner pointsbased on the following operations.

In a first operation (e.g., Operation 1), a device or module mayconstruct, sequences (e.g., N/2 short sequences) for both W⁻ and W⁺ thatare UPO compliant. The sequences may be constructed by using a binarybit weighting for the bit channels of a partition that applies a set ofweighting factors (e.g., the weighting factor for one sequence may bedifferent than another sequence, or one of the sequences may begenerated using more than one weighting factor), similar to thedescription provided above with reference to FIGS. 4 and 5.

In a second operation (e.g., Operation 2), the device or module maygenerate a bit-vector for assigning the information bits according to anMI recursion equation.

In a third operation (e.g., Operation 3), the device or module maycompare an order resulting from the bit vector to the ordercorresponding to a UPO. For any value of the bit vector that violatesthe UPO, the device or module may swap the violating value of the bitvector with an adjacent value of the bit vector (e.g., allocate thatparticular bit point to the other partition to comply with the UPO).

The device or module may repeat Operations 2 and 3 until reaching theend of the N bit sequence. This process may be performed in order togenerate a lookup table, or may be performed during encoding or decodingof a codeword.

In FIG. 11, an example of operations 1-3 is depicted. An N bit sequencein partition 1110 is being mapped to a N/2 bit sequence in partitions1115-a and 1115-b. The N bit sequence and the N/2 bits sequences mayeach also be referred to as a binary array. In the illustrated example,N=16 bits. Column 1150 is provided as a reference to show an index ofeach bit in the sequence from 15 to 0. A value of “1” in the binaryarray of partition 1110 indicates that a bit in the N bit sequence isbeing allocated to partition 1115-a, and a “0” in the binary array ofpartition 1110 indicates that a bit in the N bit sequence is beingallocated to partition 1115-b. Bit 15 has a value of 0, and,accordingly, is being allocated to bit 7 of partition 1115-b. Bit 11 hasa value of 1, and is being allocated to bit 7 of partition 1115-a. Thus,bits 4, 7, 9, 10, and 12-15 are being allocated to partition 1115-b, andbits 0-3, 5, 6, 8, and 11 are being allocated to partition 1115-a.

In an example, a 16 bit sequence has the following UPO total ordering:[15, 14, 13, 11, 7, 12, 10, 9, 6, 5, 3, 8, 4, 2, 1, 0]. This sequencemay be used in operation 1 to construct two 8 bit sequences. A bitvector generated in operation 2 has the following ordering: [15, 14, 13,11, 7, 12, 10, 6, 9, 5, 3, 8, 4, 2, 1, 0]. As can be seen at 1125 (seeFIG. 11), the order of bits 6 and 9 in the bit vector does not match theorder of bits 9 and 6 under the UPO total ordering (e.g., the bits arereversed), and hence bits 6 and 9 in the bit vector violate the UPO. Thebit causing the UPO violation in the N bit binary array of partition1110 is shaded.

To remove the UPO violation, the shaded bit may be swapped with a bit inthe N bit binary array having a value of ‘1’ immediately above (1120-a)or immediately below (1120-b), or may be swapped with any other bitinitially allocated for partition 1115-a. Swapping of a bit (e.g., anadjacent bit) is used to remedy the UPO violation. Thus, whenever a ‘0’or a ‘1’ in the bit-vector results in a violation of the UPO, theviolating bit may be swapped with the next ‘1’ or ‘0’ above or below theviolating bit (e.g., swapping a ‘0’ with a ‘1,’ or a ‘1’ with a ‘0’). Insome examples, it may be preferred to swap the violating bit with a bithaving the opposite value that is immediately below in the N bit binaryarray. In other examples, the violating bit may be swapped with the nextbit having the opposite value that is anywhere below the violating bitin the N bit binary array. Beneficially, the techniques described hereinmay provide for an improved distribution of information bits.

FIG. 12 shows a block diagram 1200 of a wireless device 1205 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Wireless device 1205 may be an example ofaspects of a base station 105 as described herein. Wireless device 1205may include receiver 1210, base station communications manager 1215, andtransmitter 1220. Wireless device 1205 may also include a processor.Each of these components may be in communication with one another (e.g.,via one or more buses).

Receiver 1210 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to informationbit distribution design, etc.). Information may be passed on to othercomponents of the device. The receiver 1210 may be an example of aspectsof the transceiver 1535 described with reference to FIG. 15. Thereceiver 1210 may utilize a single antenna or a set of antennas.

Base station communications manager 1215 may be an example of aspects ofthe base station communications manager 1515 described with reference toFIG. 15.

Base station communications manager 1215 and/or at least some of itsvarious sub-components may be implemented in hardware, software executedby a processor, firmware, or any combination thereof. If implemented insoftware executed by a processor, the functions of the base stationcommunications manager 1215 and/or at least some of its varioussub-components may be executed by a general-purpose processor, a digitalsignal processor (DSP), an application-specific integrated circuit(ASIC), a field-programmable gate array (FPGA) or other programmablelogic device, discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed in the present disclosure. The base station communicationsmanager 1215 and/or at least some of its various sub-components may bephysically located at various positions, including being distributedsuch that portions of functions are implemented at different physicallocations by one or more physical devices. In some examples, basestation communications manager 1215 and/or at least some of its varioussub-components may be a separate and distinct component in accordancewith various aspects of the present disclosure. In other examples, basestation communications manager 1215 and/or at least some of its varioussub-components may be combined with one or more other hardwarecomponents, including but not limited to an input/output (I/O)component, a transceiver, a network server, another computing device,one or more other components described in the present disclosure, or acombination thereof in accordance with various aspects of the presentdisclosure.

Base station communications manager 1215 may encode a codeword using apolar code for a transmission over a wireless channel, where thecodeword includes an information bit vector including a set ofinformation bits, and may identify a set of bit locations of the polarcode for the set of information bits. The set of bit locations may bedetermined based on a recursive partitioning of a set of bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of the each partition to bit channelsub-partitions, where at least one quantization rule is applied fordetermining whether to assign a first number of the information bits ofa first bit channel sub-partition of the bit channel sub-partitions to afixed value. Base station communications manager 1215 may transmit theencoded codeword over the wireless channel according to the polar codebased on the set of bit locations.

In some cases, the base station communications manager 1215 may alsoencode a codeword using a polar code for a transmission over a wirelesschannel, where the codeword includes an information bit vector includinga set of information bits, and may identify a set of bit locations ofthe polar code for the set of information bits. The set of bit locationsmay be determined based on a recursive partitioning of a set of bitchannels of the polar code for at least a subset of polarization stagesof the polar code, and, for each partition of the at least the subset ofthe polarization stages of the polar code, assigning portions of anumber of the information bits of the each partition to bit channelsub-partitions by adjusting the information bit allocation derived basedon the recursive partitioning to be compliant with a UPO. Base stationcommunications manager 1215 may transmit the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations.

Transmitter 1220 may transmit signals generated by other components ofthe device. In some examples, the transmitter 1220 may be collocatedwith a receiver 1210 in a transceiver module. For example, thetransmitter 1220 may be an example of aspects of the transceiver 1535described with reference to FIG. 15. The transmitter 1220 may utilize asingle antenna or a set of antennas.

FIG. 13 shows a block diagram 1300 of a wireless device 1305 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Wireless device 1305 may be an example ofaspects of a wireless device 1205 or a base station 105 as describedwith reference to FIG. 12. Wireless device 1305 may include receiver1310, base station communications manager 1315, and transmitter 1320.Wireless device 1305 may also include a processor. Each of thesecomponents may be in communication with one another (e.g., via one ormore buses).

Receiver 1310 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to informationbit distribution design, etc.). Information may be passed on to othercomponents of the device. The receiver 1310 may be an example of aspectsof the transceiver 1535 described with reference to FIG. 15. Thereceiver 1310 may utilize a single antenna or a set of antennas.

Base station communications manager 1315 may be an example of aspects ofthe base station communications manager 1515 described with reference toFIG. 15.

Base station communications manager 1315 may also include encoder 1325and bit location identifier 1330.

Encoder 1325 may encode a codeword using a polar code for a transmissionover a wireless channel, where the codeword includes an information bitvector including a set of information bits and may transmit the encodedcodeword over the wireless channel according to the polar code based ona set of bit locations.

Bit location identifier 1330 may identify the set of bit locations ofthe polar code for the set of information bits, where the set of bitlocations is determined based on a recursive partitioning of a set ofbit channels of the polar code for at least a subset of polarizationstages of the polar code, and, for each partition of the at least thesubset of the polarization stages of the polar code, assigning portionsof a number of the information bits of the each partition to bit channelsub-partitions, where at least one quantization rule is applied fordetermining whether to assign a first number of the information bits ofa first bit channel sub-partition of the bit channel sub-partitions to afixed value. Additionally or alternatively, bit location identifier 1330may identify a set of bit locations of the polar code for the set ofinformation bits, where the set of bit locations is determined based ona recursive partitioning of a set of bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof the each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO.

Transmitter 1320 may transmit signals generated by other components ofthe device. In some examples, the transmitter 1320 may be collocatedwith a receiver 1310 in a transceiver module. For example, thetransmitter 1320 may be an example of aspects of the transceiver 1535described with reference to FIG. 15. The transmitter 1320 may utilize asingle antenna or a set of antennas.

FIG. 14 shows a block diagram 1400 of a base station communicationsmanager 1415 that supports information bit distribution design inaccordance with aspects of the present disclosure. The base stationcommunications manager 1415 may be an example of aspects of a basestation communications manager 1215, 1315, or 1515 described withreference to FIGS. 12, 13, and 15. The base station communicationsmanager 1415 may include encoder 1420, bit location identifier 1425,quantization component 1430, allocator component 1435, sequenceconstructor 1440, bit vector generator 1445, comparator 1450, orderdeterminer 1455, and swapper component 1460. Each of these modules maycommunicate, directly or indirectly, with one another (e.g., via one ormore buses).

Encoder 1420 may encode a codeword using a polar code for a transmissionover a wireless channel, where the codeword includes an information bitvector including a set of information bits. Encoder 1420 mayadditionally transmit the encoded codeword over the wireless channelaccording to the polar code based on a set of bit locations.

In some cases, bit location identifier 1425 may identify the set of bitlocations of the polar code for the set of information bits, where theset of bit locations is determined based on a recursive partitioning ofa set of bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of the each partition tobit channel sub-partitions, where at least one quantization rule isapplied for determining whether to assign a first number of theinformation bits of a first bit channel sub-partition of the bit channelsub-partitions to a fixed value. In some cases, bit location identifier1425 may identify a set of bit locations of the polar code for the setof information bits, where the set of bit locations is determined basedon a recursive partitioning of a set of bit channels of the polar codefor at least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof the each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO.

Quantization component 1430 may determine a quantization rule. In somecases, a first quantization rule of the at least one quantization rulesets the first number to the fixed value as a function of a capacity ofthe first bit channel sub-partition. In some cases, the firstquantization rule applies a threshold that is dependent on a number ofbit channels of each partition. In some cases, the threshold is selectedto maintain a UPO of the bit channels of each partition. In some cases,a first quantization rule of the at least one quantization rule sets thefirst number to the fixed value as a function of a code rate of eachpartition. In some cases, the function is selected to maintain a UPO ofthe bit channels of each partition. In some cases, the fixed value is afunction of a number of bit channels of each partition. In some cases,the fixed value is equal to a number of bit channels of each partition.

Allocator component 1435 may assign, for a second partition of the eachpartitions, a second number of information bits of the second partitionto a second bit channel sub-partition of the second partition based on abaseline allocation rule. In some cases, the baseline allocation ruleapplies a floor operation to a result of a function of a capacity of thesecond bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits is less than or equal to the number of bit channels insub-partitions of the second partition. In some cases, the baselineallocation rule applies a ceiling operation to a result of a function ofa capacity of the second bit channel sub-partition and a number of bitchannels in the second bit channel sub-partition when the second numberof information bits is greater than the number of bit channels insub-partitions of the second partition.

Sequence constructor 1440 may construct a sequence for each partitionthat is compliant with the UPO. In some cases, the sequence isdetermined based on a binary bit weighting for the bit channels of eachpartition that applies a set of weighting factors.

Bit vector generator 1445 may generate a bit vector for assigning theinformation bits according to an MI recursion equation.

Comparator 1450 may compare an order resulting from the bit vector tothe UPO.

Order determiner 1455 may determine, for a value of the bit vector forat least one of the partitions, that the order resulting from the valueof the bit vector violates the UPO.

Swapper component 1460 may swap the value of the bit vector with anadjacent value of the bit vector based on identifying that the valueviolates the UPO.

FIG. 15 shows a diagram of a system 1500 including a device 1505 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Device 1505 may be an example of or includethe components of wireless device 1205, wireless device 1305, or a basestation 105 as described above, e.g., with reference to FIGS. 12 and 13.Device 1505 may include components for bi-directional voice and datacommunications including components for transmitting and receivingcommunications, including base station communications manager 1515,processor 1520, memory 1525, software 1530, transceiver 1535, antenna1540, network communications manager 1545, and inter-stationcommunications manager 1550. These components may be in electroniccommunication via one or more buses (e.g., bus 1510). Device 1505 maycommunicate wirelessly with one or more UEs 115.

Processor 1520 may include an intelligent hardware device, (e.g., ageneral-purpose processor, a DSP, a central processing unit (CPU), amicrocontroller, an ASIC, an FPGA, a programmable logic device, adiscrete gate or transistor logic component, a discrete hardwarecomponent, or any combination thereof). In some cases, processor 1520may be configured to operate a memory array using a memory controller.In other cases, a memory controller may be integrated into processor1520. Processor 1520 may be configured to execute computer-readableinstructions stored in a memory to perform various functions (e.g.,functions or tasks supporting information bit distribution design).

Memory 1525 may include random access memory (RAM) and read only memory(ROM). The memory 1525 may store computer-readable, computer-executablesoftware 1530 including instructions that, when executed, cause theprocessor to perform various functions described herein. In some cases,the memory 1525 may contain, among other things, a basic input/outputsystem (BIOS) which may control basic hardware or software operationsuch as the interaction with peripheral components or devices.

Software 1530 may include code to implement aspects of the presentdisclosure, including code to support information bit distributiondesign. Software 1530 may be stored in a non-transitorycomputer-readable medium such as system memory or other memory. In somecases, the software 1530 may not be directly executable by the processorbut may cause a computer (e.g., when compiled and executed) to performfunctions described herein.

Transceiver 1535 may communicate bi-directionally, via one or moreantennas, wired, or wireless links as described above. For example, thetransceiver 1535 may represent a wireless transceiver and maycommunicate bi-directionally with another wireless transceiver. Thetransceiver 1535 may also include a modem to modulate the packets andprovide the modulated packets to the antennas for transmission, and todemodulate packets received from the antennas.

In some cases, the wireless device may include a single antenna 1540.However, in some cases the device may have more than one antenna 1540,which may be capable of concurrently transmitting or receiving multiplewireless transmissions.

Network communications manager 1545 may manage communications with thecore network (e.g., via one or more wired backhaul links). For example,the network communications manager 1545 may manage the transfer of datacommunications for client devices, such as one or more UEs 115.

Inter-station communications manager 1550 may manage communications withother base station 105, and may include a controller or scheduler forcontrolling communications with UEs 115 in cooperation with other basestations 105. For example, the inter-station communications manager 1550may coordinate scheduling for transmissions to UEs 115 for variousinterference mitigation techniques such as beamforming or jointtransmission. In some examples, inter-station communications manager1550 may provide an X2 interface within an LTE/LTE-A wirelesscommunication network technology to provide communication between basestations 105.

FIG. 16 shows a block diagram 1600 of a wireless device 1605 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Wireless device 1605 may be an example ofaspects of a UE 115 as described herein. Wireless device 1605 mayinclude receiver 1610, UE communications manager 1615, and transmitter1620. Wireless device 1605 may also include a processor. Each of thesecomponents may be in communication with one another (e.g., via one ormore buses).

Receiver 1610 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to informationbit distribution design, etc.). Information may be passed on to othercomponents of the device. The receiver 1610 may be an example of aspectsof the transceiver 1935 described with reference to FIG. 19. Thereceiver 1610 may utilize a single antenna or a set of antennas.

UE communications manager 1615 may be an example of aspects of the UEcommunications manager 1915 described with reference to FIG. 19.

UE communications manager 1615 and/or at least some of its varioussub-components may be implemented in hardware, software executed by aprocessor, firmware, or any combination thereof. If implemented insoftware executed by a processor, the functions of the UE communicationsmanager 1615 and/or at least some of its various sub-components may beexecuted by a general-purpose processor, a DSP, an ASIC, an FPGA orother programmable logic device, discrete gate or transistor logic,discrete hardware components, or any combination thereof designed toperform the functions described in the present disclosure. The UEcommunications manager 1615 and/or at least some of its varioussub-components may be physically located at various positions, includingbeing distributed such that portions of functions are implemented atdifferent physical locations by one or more physical devices. In someexamples, UE communications manager 1615 and/or at least some of itsvarious sub-components may be a separate and distinct component inaccordance with various aspects of the present disclosure. In otherexamples, UE communications manager 1615 and/or at least some of itsvarious sub-components may be combined with one or more other hardwarecomponents, including but not limited to an I/O component, atransceiver, a network server, another computing device, one or moreother components described in the present disclosure, or a combinationthereof in accordance with various aspects of the present disclosure.

UE communications manager 1615 may receive a codeword over a wirelesschannel, where the codeword is based on a set of information bitsencoded using a polar code having a set of bit channels, and mayidentify a set of bit locations of the polar code for the set ofinformation bits. The set of bit locations may be determined based on arecursive partitioning of a set of bit channels of the polar code for atleast a subset of polarization stages of the polar code, and, for eachpartition of the at least the subset of the polarization stages of thepolar code, assigning portions of a number of the information bits ofthe each partition to bit channel sub-partitions, where at least onequantization rule is applied for determining whether to assign a firstnumber of the information bits of a first bit channel partition of thebit channel partitions to a fixed value. UE communications manager 1615may decode the received codeword according to the polar code to obtainan information bit vector at the set of bit locations. Additionally oralternatively, UE communications manager 1615 may also receive acodeword over a wireless channel, where the codeword is based on a setof information bits encoded using a polar code having a set of bitchannels, and may identify a set of bit locations of the polar code forthe set of information bits. The set of bit locations may be determinedbased on a recursive partitioning of a set of bit channels of the polarcode for at least a subset of polarization stages of the polar code,and, for each partition of the at least the subset of the polarizationstages of the polar code, assigning portions of a number of theinformation bits of the each partition to bit channel sub-partitions byadjusting the information bit allocation derived based on the recursivepartitioning to be compliant with a UPO. UE communications manager 1615may decode the received codeword according to the polar code to obtainan information bit vector at the set of bit locations.

Transmitter 1620 may transmit signals generated by other components ofthe device. In some examples, the transmitter 1620 may be collocatedwith a receiver 1610 in a transceiver module. For example, thetransmitter 1620 may be an example of aspects of the transceiver 1935described with reference to FIG. 19. The transmitter 1620 may utilize asingle antenna or a set of antennas.

FIG. 17 shows a block diagram 1700 of a wireless device 1705 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Wireless device 1705 may be an example ofaspects of a wireless device 1605 or a UE 115 as described withreference to FIG. 16. Wireless device 1705 may include receiver 1710, UEcommunications manager 1715, and transmitter 1720. Wireless device 1705may also include a processor. Each of these components may be incommunication with one another (e.g., via one or more buses).

Receiver 1710 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to informationbit distribution design, etc.). Information may be passed on to othercomponents of the device. The receiver 1710 may be an example of aspectsof the transceiver 1935 described with reference to FIG. 19. Thereceiver 1710 may utilize a single antenna or a set of antennas.

UE communications manager 1715 may be an example of aspects of the UEcommunications manager 1915 described with reference to FIG. 19. UEcommunications manager 1715 may also include decoder 1725 and bitlocation identifier 1730.

Decoder 1725 may receive a codeword over a wireless channel, where thecodeword is based on a set of information bits encoded using a polarcode having a set of bit channels, and may decode the received codewordaccording to the polar code to obtain an information bit vector at a setof bit locations.

Bit location identifier 1730 may identify the set of bit locations ofthe polar code for the set of information bits, where the set of bitlocations is determined based on a recursive partitioning of a set ofbit channels of the polar code for at least a subset of polarizationstages of the polar code, and, for each partition of the at least thesubset of the polarization stages of the polar code, assigning portionsof a number of the information bits of the each partition to bit channelsub-partitions, where at least one quantization rule is applied fordetermining whether to assign a first number of the information bits ofa first bit channel partition of the bit channel partitions to a fixedvalue. Additionally or alternatively, bit location identifier 1730 mayidentify a set of bit locations of the polar code for the set ofinformation bits, where the set of bit locations is determined based ona recursive partitioning of a set of bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof the each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO.

Transmitter 1720 may transmit signals generated by other components ofthe device. In some examples, the transmitter 1720 may be collocatedwith a receiver 1710 in a transceiver module. For example, thetransmitter 1720 may be an example of aspects of the transceiver 1935described with reference to FIG. 19. The transmitter 1720 may utilize asingle antenna or a set of antennas.

FIG. 18 shows a block diagram 1800 of a UE communications manager 1815that supports information bit distribution design in accordance withaspects of the present disclosure. The UE communications manager 1815may be an example of aspects of a UE communications manager 1615, 1715,or 1915 described with reference to FIGS. 16, 17, and 19. The UEcommunications manager 1815 may include decoder 1820, bit locationidentifier 1825, quantization component 1830, allocator component 1835,sequence constructor 1840, bit vector generator 1845, comparator 1850,order determiner 1855, and swapper component 1860. Each of these modulesmay communicate, directly or indirectly, with one another (e.g., via oneor more buses).

Decoder 1820 may receive a codeword over a wireless channel, where thecodeword is based on a set of information bits encoded using a polarcode having a set of bit channels. Decoder 1820 may also decode thereceived codeword according to the polar code to obtain an informationbit vector at a set of bit locations.

In some cases, bit location identifier 1825 may identify the set of bitlocations of the polar code for the set of information bits, where theset of bit locations is determined based on a recursive partitioning ofa set of bit channels of the polar code for at least a subset ofpolarization stages of the polar code, and, for each partition of the atleast the subset of the polarization stages of the polar code, assigningportions of a number of the information bits of the each partition tobit channel sub-partitions, where at least one quantization rule isapplied for determining whether to assign a first number of theinformation bits of a first bit channel partition of the bit channelpartitions to a fixed value. In some cases, bit location identifier 1825may identify a set of bit locations of the polar code for the set ofinformation bits, where the set of bit locations is determined based ona recursive partitioning of a set of bit channels of the polar code forat least a subset of polarization stages of the polar code, and, foreach partition of the at least the subset of the polarization stages ofthe polar code, assigning portions of a number of the information bitsof the each partition to bit channel sub-partitions by adjusting theinformation bit allocation derived based on the recursive partitioningto be compliant with a UPO.

Quantization component 1830 may determine a quantization rule. In somecases, a first quantization rule of the at least one quantization rulesets the first number to the fixed value as a function of a capacity ofthe first bit channel partition. In some cases, the first quantizationrule applies a threshold that is dependent on a number of bit channelsof each partition. In some cases, the threshold is selected to maintaina UPO of the bit channels of each partition. In some cases, a firstquantization rule of the at least one quantization rule sets the firstnumber to the fixed value as a function of a code rate of eachpartition. In some cases, the function is selected to maintain a UPO ofthe bit channels of each partition. In some cases, the fixed value is afunction of a number of bit channels of each partition. In some cases,the fixed value is equal to a number of bit channels of each partition.

Allocator component 1835 may assign, for a second partition of thepartitions, a second number of information bits of the second partitionto a second bit channel sub-partition of the second partition based on abaseline allocation rule. In some cases, the baseline allocation ruleapplies a floor operation to a result of a function of a capacity of thesecond bit channel sub-partition and a number of bit channels in thesecond bit channel sub-partition when the second number of informationbits is less than or equal to the number of bit channels insub-partitions of the second partition. In some cases, the baselineallocation rule applies a ceiling operation to a result of a function ofa capacity of the second bit channel sub-partition and a number of bitchannels in the second bit channel sub-partition when the second numberof information bits is greater than the number of bit channels insub-partitions of the second partition.

Sequence constructor 1840 may construct a sequence for each partitionthat is compliant with the UPO. In some cases, the sequence isdetermined based on a binary bit weighting for the bit channels of eachpartition that applies a set of weighting factors.

Bit vector generator 1845 may generate a bit vector for assigning thenumber of the information bits according to a MI recursion equation.

Comparator 1850 may compare an order resulting from the bit vector tothe UPO.

Order determiner 1855 may determine, for a value of the bit vector forat least one of the partitions, that the order resulting from the valueof the bit vector violates the UPO.

Swapper component 1860 may swap the value of the bit vector with anadjacent value of the bit vector based on the identifying that the valueviolates the UPO.

FIG. 19 shows a diagram of a system 1900 including a device 1905 thatsupports information bit distribution design in accordance with aspectsof the present disclosure. Device 1905 may be an example of or includethe components of UE 115 as described above, e.g., with reference toFIG. 1. Device 1905 may include components for bi-directional voice anddata communications including components for transmitting and receivingcommunications, including UE communications manager 1915, processor1920, memory 1925, software 1930, transceiver 1935, antenna 1940, andI/O controller 1945. These components may be in electronic communicationvia one or more buses (e.g., bus 1910). Device 1905 may communicatewirelessly with one or more base stations 105.

Processor 1920 may include an intelligent hardware device, (e.g., ageneral-purpose processor, a DSP, a CPU, a microcontroller, an ASIC, anFPGA, a programmable logic device, a discrete gate or transistor logiccomponent, a discrete hardware component, or any combination thereof).In some cases, processor 1920 may be configured to operate a memoryarray using a memory controller. In other cases, a memory controller maybe integrated into processor 1920. Processor 1920 may be configured toexecute computer-readable instructions stored in a memory to performvarious functions (e.g., functions or tasks supporting information bitdistribution design).

Memory 1925 may include RAM and ROM. The memory 1925 may storecomputer-readable, computer-executable software 1930 includinginstructions that, when executed, cause the processor to perform variousfunctions described herein. In some cases, the memory 1925 may contain,among other things, a BIOS which may control basic hardware or softwareoperation such as the interaction with peripheral components or devices.

Software 1930 may include code to implement aspects of the presentdisclosure, including code to support information bit distributiondesign. Software 1930 may be stored in a non-transitorycomputer-readable medium such as system memory or other memory. In somecases, the software 1930 may not be directly executable by the processorbut may cause a computer (e.g., when compiled and executed) to performfunctions described herein.

Transceiver 1935 may communicate bi-directionally, via one or moreantennas, wired, or wireless links as described above. For example, thetransceiver 1935 may represent a wireless transceiver and maycommunicate bi-directionally with another wireless transceiver. Thetransceiver 1935 may also include a modem to modulate the packets andprovide the modulated packets to the antennas for transmission, and todemodulate packets received from the antennas.

In some cases, the wireless device may include a single antenna 1940.However, in some cases the device may have more than one antenna 1940,which may be capable of concurrently transmitting or receiving multiplewireless transmissions.

I/O controller 1945 may manage input and output signals for device 1905.I/O controller 1945 may also manage peripherals not integrated intodevice 1905. In some cases, I/O controller 1945 may represent a physicalconnection or port to an external peripheral. In some cases, I/Ocontroller 1945 may utilize an operating system such as iOS®, ANDROID®,MS-DOS®, MS-WINDOWS®, OS/2®, UNIX®, LINUX®, or another known operatingsystem. In other cases, I/O controller 1945 may represent or interactwith a modem, a keyboard, a mouse, a touchscreen, or a similar device.In some cases, I/O controller 1945 may be implemented as part of aprocessor. In some cases, a user may interact with device 1905 via I/Ocontroller 1945 or via hardware components controlled by I/O controller1945.

FIG. 20 shows a flowchart illustrating a method 2000 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2000 may be implemented by a basestation 105 or its components as described herein. For example, theoperations of method 2000 may be performed by a base stationcommunications manager as described with reference to FIGS. 12 through15. In some examples, a base station 105 may execute a set of codes tocontrol the functional elements of the device to perform the functionsdescribed below. Additionally or alternatively, the base station 105 mayperform aspects of the functions described below using special-purposehardware.

At 2005 the base station 105 may encode a codeword using a polar codefor a transmission over a wireless channel, where the codeword includesan information bit vector including multiple information bits. Theoperations of 2005 may be performed according to the methods describedherein. In certain examples, aspects of the operations of 2005 may beperformed by an encoder as described with reference to FIGS. 12 through15.

At 2010 the base station 105 may identify a set of bit locations of thepolar code for the multiple information bits, where the set of bitlocations is determined based on a recursive partitioning of multiplebit channels of the polar code for at least a subset of polarizationstages of the polar code, and, for each partition of the at least thesubset of the polarization stages of the polar code, assigning portionsof a number of the information bits of the each partition to bit channelsub-partitions, where at least one quantization rule is applied fordetermining whether to assign a first number of the information bits ofa first bit channel sub-partition of the bit channel sub-partitions to afixed value. The operations of 2010 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2010 may be performed by a bit location identifier as described withreference to FIGS. 12 through 15.

At 2015 the base station 105 may transmit the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations. The operations of 2015 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2015 may be performed by an encoder as described with reference toFIGS. 12 through 15.

FIG. 21 shows a flowchart illustrating a method 2100 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2100 may be implemented by a basestation 105 or its components as described herein. For example, theoperations of method 2100 may be performed by a base stationcommunications manager as described with reference to FIGS. 12 through15. In some examples, a base station 105 may execute a set of codes tocontrol the functional elements of the device to perform the functionsdescribed below. Additionally or alternatively, the base station 105 mayperform aspects of the functions described below using special-purposehardware.

At 2105 the base station 105 may encode a codeword using a polar codefor a transmission over a wireless channel, where the codeword includesan information bit vector including multiple information bits. Theoperations of 2105 may be performed according to the methods describedherein. In certain examples, aspects of the operations of 2105 may beperformed by an encoder as described with reference to FIGS. 12 through15.

At 2110 the base station 105 may identify a set of bit locations of thepolar code for the multiple information bits, where the set of bitlocations is determined based on a recursive partitioning of multiplebit channels of the polar code for at least a subset of polarizationstages of the polar code, and, for each partition of the at least thesubset of the polarization stages of the polar code, assigning portionsof a number of the information bits of the each partition to bit channelsub-partitions by adjusting the information bit allocation derived basedon the recursive partitioning to be compliant with a UPO. The operationsof 2110 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 2110 may be performed bya bit location identifier as described with reference to FIGS. 12through 15.

At 2115 the base station 105 may transmit the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations. The operations of 2115 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2115 may be performed by an encoder as described with reference toFIGS. 12 through 15.

FIG. 22 shows a flowchart illustrating a method 2200 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2200 may be implemented by a basestation 105 or its components as described herein. For example, theoperations of method 2200 may be performed by a base stationcommunications manager as described with reference to FIGS. 12 through15. In some examples, a base station 105 may execute a set of codes tocontrol the functional elements of the device to perform the functionsdescribed below. Additionally or alternatively, the base station 105 mayperform aspects of the functions described below using special-purposehardware.

At 2205 the base station 105 may encode a codeword using a polar codefor a transmission over a wireless channel, where the codeword includesan information bit vector including multiple information bits. Theoperations of 2205 may be performed according to the methods describedherein. In certain examples, aspects of the operations of 2205 may beperformed by an encoder as described with reference to FIGS. 12 through15.

At 2210 the base station 105 may identify a set of bit locations of thepolar code for the multiple information bits, where the set of bitlocations is determined based on a recursive partitioning of multiplebit channels of the polar code for at least a subset of polarizationstages of the polar code, and, for each partition of the at least thesubset of the polarization stages of the polar code, assigning portionsof a number of the information bits of the each partition to bit channelsub-partitions by adjusting the information bit allocation derived basedon the recursive partitioning to be compliant with a UPO by constructinga sequence for the each partition that is compliant with the UPO,generating a bit vector for assigning the number of the information bitsaccording to an MI recursion equation, and comparing an order resultingfrom the bit vector to the UPO. The operations of 2210 may be performedaccording to the methods described herein. In certain examples, aspectsof the operations of 2210 may be performed by a bit location identifieras described with reference to FIGS. 12 through 15.

At 2215 the base station 105 may transmit the encoded codeword over thewireless channel according to the polar code based on the set of bitlocations. The operations of 2215 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2215 may be performed by an encoder as described with reference toFIGS. 12 through 15.

FIG. 23 shows a flowchart illustrating a method 2300 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2300 may be implemented by a UE 115or its components as described herein. For example, the operations ofmethod 2300 may be performed by a UE communications manager as describedwith reference to FIGS. 16 through 19. In some examples, a UE 115 mayexecute a set of codes to control the functional elements of the deviceto perform the functions described below. Additionally or alternatively,the UE 115 may perform aspects of the functions described below usingspecial-purpose hardware.

At 2305 the UE 115 may receive a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels. The operations of 2305 may beperformed according to the methods described herein. In certainexamples, aspects of the operations of 2305 may be performed by adecoder as described with reference to FIGS. 16 through 19.

At 2310 the UE 115 may identify a set of bit locations of the polar codefor the multiple information bits, where the set of bit locations isdetermined based on a recursive partitioning of multiple bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of the each partition to bit channelsub-partitions, where at least one quantization rule is applied fordetermining whether to assign a first number of the information bits ofa first bit channel partition of the bit channel partitions to a fixedvalue. The operations of 2310 may be performed according to the methodsdescribed herein. In certain examples, aspects of the operations of 2310may be performed by a bit location identifier as described withreference to FIGS. 16 through 19.

At 2315 the UE 115 may decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations. The operations of 2315 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2315 may be performed by a decoder as described with reference toFIGS. 16 through 19.

FIG. 24 shows a flowchart illustrating a method 2400 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2400 may be implemented by a UE 115or its components as described herein. For example, the operations ofmethod 2400 may be performed by a UE communications manager as describedwith reference to FIGS. 16 through 19. In some examples, a UE 115 mayexecute a set of codes to control the functional elements of the deviceto perform the functions described below. Additionally or alternatively,the UE 115 may perform aspects of the functions described below usingspecial-purpose hardware.

At 2405 the UE 115 may receive a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels. The operations of 2405 may beperformed according to the methods described herein. In certainexamples, aspects of the operations of 2405 may be performed by adecoder as described with reference to FIGS. 16 through 19.

At 2410 the UE 115 may identify a set of bit locations of the polar codefor the multiple information bits, where the set of bit locations isdetermined based on a recursive partitioning of multiple bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of the each partition to bit channel sub-partitionsby adjusting the information bit allocation derived based on therecursive partitioning to be compliant with a UPO. The operations of2410 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 2410 may be performed bya bit location identifier as described with reference to FIGS. 16through 19.

At 2415 the UE 115 may decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations. The operations of 2415 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2415 may be performed by a decoder as described with reference toFIGS. 16 through 19.

FIG. 25 shows a flowchart illustrating a method 2500 for information bitdistribution design in accordance with aspects of the presentdisclosure. The operations of method 2500 may be implemented by a UE 115or its components as described herein. For example, the operations ofmethod 2500 may be performed by a UE communications manager as describedwith reference to FIGS. 16 through 19. In some examples, a UE 115 mayexecute a set of codes to control the functional elements of the deviceto perform the functions described below. Additionally or alternatively,the UE 115 may perform aspects of the functions described below usingspecial-purpose hardware.

At 2505 the UE 115 may receive a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels. The operations of 2505 may beperformed according to the methods described herein. In certainexamples, aspects of the operations of 2505 may be performed by adecoder as described with reference to FIGS. 16 through 19.

At 2510 the UE 115 may identify a set of bit locations of the polar codefor the multiple information bits, where the set of bit locations isdetermined based on a recursive partitioning of multiple bit channels ofthe polar code for at least a subset of polarization stages of the polarcode, and, for each partition of the at least the subset of thepolarization stages of the polar code, assigning portions of a number ofthe information bits of the each partition to bit channel sub-partitionsby adjusting the information bit allocation derived based on therecursive partitioning to be compliant with a UPO by constructing asequence for the each partition that is compliant with the UPO,generating a bit vector for assigning the number of the information bitsaccording to an MI recursion equation, and comparing an order resultingfrom the bit vector to the UPO. The operations of 2510 may be performedaccording to the methods described herein. In certain examples, aspectsof the operations of 2510 may be performed by a bit location identifieras described with reference to FIGS. 16 through 19.

At 2515 the UE 115 may decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations. The operations of 2515 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 2515 may be performed by a decoder as described with reference toFIGS. 16 through 19.

FIG. 26 shows a block diagram 2600 of a wireless device 2605 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Wireless device 2605 may be an example of aspects ofa UE 115 as described herein. Wireless device 2605 may include receiver2610, UE communications manager 2615, and transmitter 2620. Wirelessdevice 2605 may also include a processor. Each of these components maybe in communication with one another (e.g., via one or more buses).

Receiver 2610 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to polarsequence design based on coefficient reliability and improvedinformation bit distribution, etc.). Information may be passed on toother components of the device. The receiver 2610 may be an example ofaspects of the transceiver 2935 described with reference to FIG. 29. Thereceiver 2610 may utilize a single antenna or a set of antennas.

UE communications manager 2615 may be an example of aspects of the UEcommunications manager 2915 described with reference to FIG. 29.

UE communications manager 2615 and/or at least some of its varioussub-components may be implemented in hardware, software executed by aprocessor, firmware, or any combination thereof. If implemented insoftware executed by a processor, the functions of the UE communicationsmanager 2615 and/or at least some of its various sub-components may beexecuted by a general-purpose processor, a DSP, an ASIC, an FPGA orother programmable logic device, discrete gate or transistor logic,discrete hardware components, or any combination thereof designed toperform the functions described in the present disclosure. The UEcommunications manager 2615 and/or at least some of its varioussub-components may be physically located at various positions, includingbeing distributed such that portions of functions are implemented atdifferent physical locations by one or more physical devices. In someexamples, UE communications manager 2615 and/or at least some of itsvarious sub-components may be a separate and distinct component inaccordance with various aspects of the present disclosure. In otherexamples, UE communications manager 2615 and/or at least some of itsvarious sub-components may be combined with one or more other hardwarecomponents, including but not limited to an I/O component, atransceiver, a network server, another computing device, one or moreother components described in the present disclosure, or a combinationthereof in accordance with various aspects of the present disclosure.

UE communications manager 2615 may receive a codeword over a wirelesschannel, where the codeword is based on a set of information bitsencoded using a polar code having a set of bit channels, identify a setof bit locations of the set of bit channels of the polar code for theset of information bits based on a bit index reliability sequence, wherethe bit index reliability sequence is determined based on a binary bitweighting for the set of bit channels that applies a set of weightingfactors, and decode the received codeword according to the polar code toobtain an information bit vector at the set of bit locations. The UEcommunications manager 2615 may also receive a codeword over a wirelesschannel, where the codeword is based on a set of information bitsencoded using a polar code having a set of bit channels, select a bitindex reliability sequence for the set of bit channels based on a lengthof the codeword, where an order of bit indices in the bit indexreliability sequence is determined based on applying a UPO to an inputsearch sequence to obtain a partial order, applying an analytical methodto obtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders, anddecode the codeword based on the bit index reliability sequence.

Transmitter 2620 may transmit signals generated by other components ofthe device. In some examples, the transmitter 2620 may be collocatedwith a receiver 2610 in a transceiver module. For example, thetransmitter 2620 may be an example of aspects of the transceiver 2935described with reference to FIG. 29. The transmitter 2620 may utilize asingle antenna or a set of antennas.

FIG. 27 shows a block diagram 2700 of a wireless device 2705 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Wireless device 2705 may be an example of aspects ofa wireless device 2605 or a UE 115 as described with reference to FIG.26. Wireless device 2705 may include receiver 2710, UE communicationsmanager 2715, and transmitter 2720. Wireless device 2705 may alsoinclude a processor. Each of these components may be in communicationwith one another (e.g., via one or more buses).

Receiver 2710 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to polarsequence design based on coefficient reliability and improvedinformation bit distribution, etc.). Information may be passed on toother components of the device. The receiver 2710 may be an example ofaspects of the transceiver 2935 described with reference to FIG. 29. Thereceiver 2710 may utilize a single antenna or a set of antennas.

UE communications manager 2715 may be an example of aspects of the UEcommunications manager 2915 described with reference to FIG. 29. UEcommunications manager 2715 may also include codeword processor 2725,bit location identifier 2730, decoder 2735, and sequence identifier2740.

Codeword processor 2725 may receive a codeword over a wireless channel,where the codeword is based on a set of information bits encoded using apolar code having a set of bit channels.

Bit location identifier 2730 may identify a set of bit locations of theset of bit channels of the polar code for the set of information bitsbased on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe set of bit channels that applies a set of weighting factors.

Decoder 2735 may decode the received codeword according to the polarcode to obtain an information bit vector at the set of bit locations. Insome cases, decoder 2735 may decode the codeword based on the bit indexreliability sequence. In some cases, decoding the codeword includesapplying a successive cancellation list decoding algorithm to a signalthat includes the codeword.

Sequence identifier 2740 may select a bit index reliability sequence forthe set of bit channels based on a length of the codeword, where anorder of bit indices in the bit index reliability sequence is determinedbased on applying a UPO to an input search sequence to obtain a partialorder, applying an analytical method to obtain calculated relativeorders of bit indices not ordered in the partial order, and applying asimulation to refine an order of at least two bit indices selected basedon the calculated relative orders. In some cases, sequence identifier2740 may add a selected bit index to the bit index reliability sequence,calculate a second partial order under the UPO of an input searchsubsequence, and/or select a bit index from the input search subsequencebased on the second partial order. In some cases, the UPO includes afirst property and a second property, where the calculated relativeorders of bit indices violate at least one of the first property or thesecond property. In some cases, the simulation is a link-levelperformance simulation.

In some cases, the simulation is based on a list size applied by thesuccessive cancellation list decoding algorithm. In some cases, theorder of bit indices in the bit index reliability sequence is determinedbased on selecting a bit index from the input search sequence based onthe partial order. In some cases, the analytical method is an indexpolarization weight rule, or a Reed-Muller rule, or a DE rule, or anMI-DE rule, or any combination thereof.

Transmitter 2720 may transmit signals generated by other components ofthe device. In some examples, the transmitter 2720 may be collocatedwith a receiver 2710 in a transceiver module. For example, thetransmitter 2720 may be an example of aspects of the transceiver 2935described with reference to FIG. 29. The transmitter 2720 may utilize asingle antenna or a set of antennas.

FIG. 28 shows a block diagram 2800 of a UE communications manager 2815that supports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. The UE communications manager 2815 may be an exampleof aspects of a UE communications manager 2615, 2715, or 2915 describedwith reference to FIGS. 26, 27, and 29. The UE communications manager2815 may include codeword processor 2820, bit location identifier 2825,decoder 2830, sequence identifier 2835, bit weighting component 2840,sequence modifier 2845, and bit index remover 2850. Each of thesemodules may communicate, directly or indirectly, with one another (e.g.,via one or more buses).

Codeword processor 2820 may receive a codeword over a wireless channel,where the codeword is based on a set of information bits encoded using apolar code having a set of bit channels.

Bit location identifier 2825 may identify a set of bit locations of theset of bit channels of the polar code for the set of information bitsbased on a bit index reliability sequence, where the bit indexreliability sequence may be determined based on a binary bit weightingfor the set of bit channels that applies a set of weighting factors.

Decoder 2830 may decode the received codeword according to the polarcode to obtain an information bit vector at the set of bit locationsand/or may decode the codeword based on the bit index reliabilitysequence. In some cases, decoding the codeword includes applyingsuccessive cancellation list decoding algorithm(s) to a signal thatincludes the codeword.

Sequence identifier 2835 may select a bit index reliability sequence forthe set of bit channels based on a length of the codeword, where anorder of bit indices in the bit index reliability sequence is determinedbased on applying a UPO to an input search sequence to obtain a partialorder, applying an analytical method to obtain calculated relativeorders of bit indices not ordered in the partial order, and applying asimulation to refine an order of at least two bit indices selected basedon the calculated relative orders. In some cases, sequence identifier2835 may add a selected bit index to the bit index reliability sequence,calculate a second partial order under the UPO of the input searchsubsequence, and/or select a bit index from the input search subsequencebased on the second partial order. In some cases, the UPO includes afirst property and a second property, where the calculated relativeorders of bit indices violate at least one of the first property or thesecond property. In some cases, the simulation is a link-levelperformance simulation.

In some cases, the simulation is based on a list size applied by thesuccessive cancellation list decoding algorithm. In some cases, theorder of bit indices in the reliability sequence is determined based onselecting a bit index from the input search sequence based on thepartial order. In some cases, the analytical method is an indexpolarization weight rule, or a Reed-Muller rule, or a DE rule, or anMI-DE rule, or any combination thereof.

Bit weighting component 2840 may determine the bit index reliabilitysequence by performing the binary bit weighting using a first weightingfactor to obtain a first reliability sequence for the set of bitchannels. In some cases, the bit index reliability sequence isdetermined by performing the binary bit weighting using a firstweighting factor for a first subset of bit indices and a secondweighting factor for a second subset of bit indices. In some cases, thebit index reliability sequence is determined by performing the binarybit weighting using a third weighting factor for a third subset of bitindices.

Sequence modifier 2845 may modify a subset of the first reliabilitysequence by performing the binary bit weighting using a second weightingfactor to obtain a second reliability sequence for the subset of thefirst reliability sequence. In some cases, the bit index reliabilitysequence is determined by modifying a subset of the second reliabilitysequence by performing the binary bit weighting using a third weightingfactor to obtain a third reliability sequence for the subset of thesecond reliability sequence. In some cases, the subset of the firstreliability sequence includes the set of bit channels having lowestbit-channel indices in the first reliability sequence. In some cases,the subset of the first reliability sequence includes the set of bitchannels having highest bit-channel indices in the first reliabilitysequence. In some cases, sequence modifier 2845 may modify a portion ofthe bit index reliability sequence using a second sequence to generate amodified bit index reliability sequence, where decoding the codewordincludes decoding the codeword based on the modified bit indexreliability sequence.

Bit index remover 2850 may remove the selected bit index from the inputsearch sequence to generate an input search subsequence.

FIG. 29 shows a diagram of a system 2900 including a device 2905 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Device 2905 may be an example of or include thecomponents of wireless device 2605, wireless device 2705, or a UE 115 asdescribed above, e.g., with reference to FIGS. 26 and 27. Device 2905may include components for bi-directional voice and data communicationsincluding components for transmitting and receiving communications,including UE communications manager 2915, processor 2920, memory 2925,software 2930, transceiver 2935, antenna 2940, and I/O controller 2945.These components may be in electronic communication via one or morebuses (e.g., bus 2910). Device 2905 may communicate wirelessly with oneor more base stations 105.

Processor 2920 may include an intelligent hardware device, (e.g., ageneral-purpose processor, a DSP, a CPU, a microcontroller, an ASIC, anFPGA, a programmable logic device, a discrete gate or transistor logiccomponent, a discrete hardware component, or any combination thereof).In some cases, processor 2920 may be configured to operate a memoryarray using a memory controller. In other cases, a memory controller maybe integrated into processor 2920. Processor 2920 may be configured toexecute computer-readable instructions stored in a memory to performvarious functions (e.g., functions or tasks supporting polar sequencedesign based on coefficient reliability and improved information bitdistribution).

Memory 2925 may include RAM and ROM. The memory 2925 may storecomputer-readable, computer-executable software 2930 includinginstructions that, when executed, cause the processor to perform variousfunctions described herein. In some cases, the memory 2925 may contain,among other things, a BIOS which may control basic hardware or softwareoperation such as the interaction with peripheral components or devices.

Software 2930 may include code to implement aspects of the presentdisclosure, including code to support polar sequence design based oncoefficient reliability and improved information bit distribution.Software 2930 may be stored in a non-transitory computer-readable mediumsuch as system memory or other memory. In some cases, the software 2930may not be directly executable by the processor but may cause a computer(e.g., when compiled and executed) to perform functions describedherein.

Transceiver 2935 may communicate bi-directionally, via one or moreantennas, wired, or wireless links as described above. For example, thetransceiver 2935 may represent a wireless transceiver and maycommunicate bi-directionally with another wireless transceiver. Thetransceiver 2935 may also include a modem to modulate the packets andprovide the modulated packets to the antennas for transmission, and todemodulate packets received from the antennas.

In some cases, the wireless device may include a single antenna 2940.However, in some cases the device may have more than one antenna 2940,which may be capable of concurrently transmitting or receiving multiplewireless transmissions.

I/O controller 2945 may manage input and output signals for device 2905.I/O controller 2945 may also manage peripherals not integrated intodevice 2905. In some cases, I/O controller 2945 may represent a physicalconnection or port to an external peripheral. In some cases, I/Ocontroller 2945 may utilize an operating system such as iOS®, ANDROID®,MS-DOS®, MS-WINDOWS®, OS/2®, UNIX®, LINUX®, or another known operatingsystem. In other cases, I/O controller 2945 may represent or interactwith a modem, a keyboard, a mouse, a touchscreen, or a similar device.In some cases, I/O controller 2945 may be implemented as part of aprocessor. In some cases, a user may interact with device 2905 via I/Ocontroller 2945 or via hardware components controlled by I/O controller2945.

FIG. 30 shows a block diagram 3000 of a wireless device 3005 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Wireless device 3005 may be an example of aspects ofa base station 105 as described herein. Wireless device 3005 may includereceiver 3010, base station communications manager 3015, and transmitter3020. Wireless device 3005 may also include a processor. Each of thesecomponents may be in communication with one another (e.g., via one ormore buses).

Receiver 3010 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to polarsequence design based on coefficient reliability and improvedinformation bit distribution, etc.). Information may be passed on toother components of the device. The receiver 3010 may be an example ofaspects of the transceiver 3335 described with reference to FIG. 33. Thereceiver 3010 may utilize a single antenna or a set of antennas.

Base station communications manager 3015 may be an example of aspects ofthe base station communications manager 3315 described with reference toFIG. 33.

Base station communications manager 3015 and/or at least some of itsvarious sub-components may be implemented in hardware, software executedby a processor, firmware, or any combination thereof. If implemented insoftware executed by a processor, the functions of the base stationcommunications manager 3015 and/or at least some of its varioussub-components may be executed by a general-purpose processor, a DSP, anASIC, an FPGA or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions described in the presentdisclosure. The base station communications manager 3015 and/or at leastsome of its various sub-components may be physically located at variouspositions, including being distributed such that portions of functionsare implemented at different physical locations by one or more physicaldevices. In some examples, base station communications manager 3015and/or at least some of its various sub-components may be a separate anddistinct component in accordance with various aspects of the presentdisclosure. In other examples, base station communications manager 3015and/or at least some of its various sub-components may be combined withone or more other hardware components, including but not limited to anI/O component, a transceiver, a network server, another computingdevice, one or more other components described in the presentdisclosure, or a combination thereof in accordance with various aspectsof the present disclosure.

Base station communications manager 3015 may identify a set ofinformation bits for encoding using a polar code having a set of bitchannels, and may identify a set of bit locations of the set of bitchannels of the polar code for the set of information bits based on abit index reliability sequence, where the bit index reliability sequencemay be determined based on a binary bit weighting for the set of bitchannels that applies a set of weighting factors. Base stationcommunications manager 3015 may generate a codeword according to thepolar code based on the bit index reliability sequence and the set ofinformation bits, and transmit the codeword. Additionally oralternatively, base station communications manager 3015 may determine abit index reliability sequence for a set of bit channels of a polar codebased on a length of a codeword, where an order of bit indices in thereliability sequence is determined based on applying a UPO to an inputsearch sequence to obtain a partial order, applying an analytical methodto obtain calculated relative orders of bit indices not ordered in thepartial order, and applying a simulation to refine an order of at leasttwo bit indices selected based on the calculated relative orders. Basestation communications manager 3015 may generate the codeword accordingto the polar code based on the bit index reliability sequence and a setof information bits encoded using the polar code, and may transmit thecodeword.

Transmitter 3020 may transmit signals generated by other components ofthe device. In some examples, the transmitter 3020 may be collocatedwith a receiver 3010 in a transceiver module. For example, thetransmitter 3020 may be an example of aspects of the transceiver 3335described with reference to FIG. 33. The transmitter 3020 may utilize asingle antenna or a set of antennas.

FIG. 31 shows a block diagram 3100 of a wireless device 3105 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Wireless device 3105 may be an example of aspects ofa wireless device 3005 or a base station 105 as described with referenceto FIG. 30. Wireless device 3105 may include receiver 3110, base stationcommunications manager 3115, and transmitter 3120. Wireless device 3105may also include a processor. Each of these components may be incommunication with one another (e.g., via one or more buses).

Receiver 3110 may receive information such as packets, user data, orcontrol information associated with various information channels (e.g.,control channels, data channels, and information related to polarsequence design based on coefficient reliability and improvedinformation bit distribution, etc.). Information may be passed on toother components of the device. The receiver 3110 may be an example ofaspects of the transceiver 3335 described with reference to FIG. 33. Thereceiver 3110 may utilize a single antenna or a set of antennas.

Base station communications manager 3115 may be an example of aspects ofthe base station communications manager 3315 described with reference toFIG. 33. Base station communications manager 3115 may also includeinformation bit component 3125, bit location identifier 3130, codewordprocessor 3135, and sequence identifier 3140.

Information bit component 3125 may identify a set of information bitsfor encoding using a polar code having a set of bit channels.

Bit location identifier 3130 may identify a set of bit locations of theset of bit channels of the polar code for the set of information bitsbased on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe set of bit channels that applies a set of weighting factors.

In some cases, codeword processor 3135 may generate a codeword accordingto the polar code based on the bit index reliability sequence and theset of information bits, and may transmit the codeword. In other cases,codeword processor 3135 may generate the codeword according to the polarcode based on the bit index reliability sequence and a set ofinformation bits encoded using the polar code, and may transmit thecodeword.

Sequence identifier 3140 may determine a bit index reliability sequencefor a set of bit channels of a polar code based on a length of acodeword, where an order of bit indices in the reliability sequence isdetermined based on applying a UPO to an input search sequence to obtaina partial order, applying an analytical method to obtain calculatedrelative orders of bit indices not ordered in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated relative orders.

Transmitter 3120 may transmit signals generated by other components ofthe device. In some examples, the transmitter 3120 may be collocatedwith a receiver 3110 in a transceiver module. For example, thetransmitter 3120 may be an example of aspects of the transceiver 3335described with reference to FIG. 33. The transmitter 3120 may utilize asingle antenna or a set of antennas.

FIG. 32 shows a block diagram 3200 of a base station communicationsmanager 3215 that supports polar sequence design based on coefficientreliability and improved information bit distribution in accordance withaspects of the present disclosure. The base station communicationsmanager 3215 may be an example of aspects of a base stationcommunications manager 3315 described with reference to FIGS. 30, 31,and 33. The base station communications manager 3215 may includeinformation bit component 3220, bit location identifier 3225, codewordprocessor 3230, sequence identifier 3235, bit weighting component 3240,and sequence modifier 3245. Each of these modules may communicate,directly or indirectly, with one another (e.g., via one or more buses).

Information bit component 3220 may identify a set of information bitsfor encoding using a polar code having a set of bit channels.

Bit location identifier 3225 may identify a set of bit locations of theset of bit channels of the polar code for the set of information bitsbased on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe set of bit channels that applies a set of weighting factors.

Codeword processor 3230 may generate a codeword according to the polarcode based on the bit index reliability sequence and the set ofinformation bits, and may transmit the codeword.

Sequence identifier 3235 may determine a bit index reliability sequencefor a set of bit channels of a polar code based on a length of acodeword, where an order of bit indices in the reliability sequence isdetermined based on applying a UPO to an input search sequence to obtaina partial order, applying an analytical method to obtain calculatedrelative orders of bit indices not ordered in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated relative orders.

Bit weighting component 3240 may determine the bit index reliabilitysequence by performing the binary bit weighting using a first weightingfactor to obtain a first reliability sequence for the set of bitchannels. In some cases, the bit index reliability sequence isdetermined by performing the binary bit weighting using a firstweighting factor for a first subset of bit indices and a secondweighting factor for a second subset of bit indices. In some cases, thebit index reliability sequence is determined by performing the binarybit weighting using a third weighting factor for a third subset of bitindices.

Sequence modifier 3245 may modify a subset of the first reliabilitysequence by performing the binary bit weighting using a second weightingfactor to obtain a second reliability sequence for the subset of thefirst reliability sequence. In some cases, the bit index reliabilitysequence is determined by modifying a subset of the second reliabilitysequence by performing the binary bit weighting using a third weightingfactor to obtain a third reliability sequence for the subset of thesecond reliability sequence. In some cases, the subset of the firstreliability sequence includes the set of bit channels having lowestbit-channel indices in the first reliability sequence. In other cases,the subset of the first reliability sequence includes the set of bitchannels having highest bit-channel indices in the first reliabilitysequence.

FIG. 33 shows a diagram of a system 3300 including a device 3305 thatsupports polar sequence design based on coefficient reliability andimproved information bit distribution in accordance with aspects of thepresent disclosure. Device 3305 may be an example of or include thecomponents of base station 105 as described above, e.g., with referenceto FIG. 1. Device 3305 may include components for bi-directional voiceand data communications including components for transmitting andreceiving communications, including base station communications manager3315, processor 3320, memory 3325, software 3330, transceiver 3335,antenna 3340, network communications manager 3345, and inter-stationcommunications manager 3350. These components may be in electroniccommunication via one or more buses (e.g., bus 3310). Device 3305 maycommunicate wirelessly with one or more UEs 115.

Processor 3320 may include an intelligent hardware device, (e.g., ageneral-purpose processor, a DSP, a CPU, a microcontroller, an ASIC, anFPGA, a programmable logic device, a discrete gate or transistor logiccomponent, a discrete hardware component, or any combination thereof).In some cases, processor 3320 may be configured to operate a memoryarray using a memory controller. In other cases, a memory controller maybe integrated into processor 3320. Processor 3320 may be configured toexecute computer-readable instructions stored in a memory to performvarious functions (e.g., functions or tasks supporting polar sequencedesign based on coefficient reliability and improved information bitdistribution).

Memory 3325 may include RAM and ROM. The memory 3325 may storecomputer-readable, computer-executable software 3330 includinginstructions that, when executed, cause the processor to perform variousfunctions described herein. In some cases, the memory 3325 may contain,among other things, a BIOS which may control basic hardware or softwareoperation such as the interaction with peripheral components or devices.

Software 3330 may include code to implement aspects of the presentdisclosure, including code to support polar sequence design based oncoefficient reliability and improved information bit distribution.Software 3330 may be stored in a non-transitory computer-readable mediumsuch as system memory or other memory. In some cases, the software 3330may not be directly executable by the processor but may cause a computer(e.g., when compiled and executed) to perform functions describedherein.

Transceiver 3335 may communicate bi-directionally, via one or moreantennas, wired, or wireless links as described above. For example, thetransceiver 3335 may represent a wireless transceiver and maycommunicate bi-directionally with another wireless transceiver. Thetransceiver 3335 may also include a modem to modulate the packets andprovide the modulated packets to the antennas for transmission, and todemodulate packets received from the antennas.

In some cases, the wireless device may include a single antenna 3340.However, in some cases the device may have more than one antenna 3340,which may be capable of concurrently transmitting or receiving multiplewireless transmissions.

Network communications manager 3345 may manage communications with thecore network (e.g., via one or more wired backhaul links). For example,the network communications manager 3345 may manage the transfer of datacommunications for client devices, such as one or more UEs 115.

Inter-station communications manager 3350 may manage communications withother base station 105, and may include a controller or scheduler forcontrolling communications with UEs 115 in cooperation with other basestations 105. For example, the inter-station communications manager 3350may coordinate scheduling for transmissions to UEs 115 for variousinterference mitigation techniques such as beamforming or jointtransmission. In some examples, inter-station communications manager3350 may provide an X2 interface within an LTE/LTE-A wirelesscommunication network technology to provide communication between basestations 105.

FIG. 34 shows a flowchart illustrating a method 3400 for polar sequencedesign based on coefficient reliability and improved information bitdistribution in accordance with aspects of the present disclosure. Theoperations of method 3400 may be implemented by a UE 115 or itscomponents as described herein. For example, the operations of method3400 may be performed by a UE communications manager as described withreference to FIGS. 26 through 29. In some examples, a UE 115 may executea set of codes to control the functional elements of the device toperform the functions described below. Additionally or alternatively,the UE 115 may perform aspects of the functions described below usingspecial-purpose hardware.

At 3405 the UE 115 may receive a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels. The operations of 3405 may beperformed according to the methods described herein. In certainexamples, aspects of the operations of 3405 may be performed by acodeword processor as described with reference to FIGS. 26 through 29.

At 3410 the UE 115 may identify a set of bit locations of the multiplebit channels of the polar code for the multiple information bits basedon a bit index reliability sequence, where the bit index reliabilitysequence is determined based on a binary bit weighting for the multiplebit channels that applies multiple weighting factors. The operations of3410 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 3410 may be performed bya bit location identifier as described with reference to FIGS. 26through 29.

At 3415 the UE 115 may decode the received codeword according to thepolar code to obtain an information bit vector at the set of bitlocations. The operations of 3415 may be performed according to themethods described herein. In certain examples, aspects of the operationsof 3415 may be performed by a decoder as described with reference toFIGS. 26 through 29.

FIG. 35 shows a flowchart illustrating a method 3500 for polar sequencedesign based on coefficient reliability and improved information bitdistribution in accordance with aspects of the present disclosure. Theoperations of method 3500 may be implemented by a base station 105 orits components as described herein. For example, the operations ofmethod 3500 may be performed by a base station communications manager asdescribed with reference to FIGS. 30 through 33. In some examples, abase station 105 may execute a set of codes to control the functionalelements of the device to perform the functions described below.Additionally or alternatively, the base station 105 may perform aspectsof the functions described below using special-purpose hardware.

At 3505 the base station 105 may identify multiple information bits forencoding using a polar code having multiple bit channels. The operationsof 3505 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 3505 may be performed byan information bit component as described with reference to FIGS. 30through 33.

At 3510 the base station 105 may identify a set of bit locations of themultiple bit channels of the polar code for the multiple informationbits based on a bit index reliability sequence, where the bit indexreliability sequence is determined based on a binary bit weighting forthe multiple bit channels that applies multiple weighting factors. Theoperations of 3510 may be performed according to the methods describedherein. In certain examples, aspects of the operations of 3510 may beperformed by a bit location identifier as described with reference toFIGS. 30 through 33.

At 3515 the base station 105 may generate a codeword according to thepolar code based on the bit index reliability sequence and the multipleinformation bits. The operations of 3515 may be performed according tothe methods described herein. In certain examples, aspects of theoperations of 3515 may be performed by a codeword processor as describedwith reference to FIGS. 30 through 33.

At 3520 the base station 105 may transmit the codeword. The operationsof 3520 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 3520 may be performed bya codeword processor as described with reference to FIGS. 30 through 33.

FIG. 36 shows a flowchart illustrating a method 3600 for polar sequencedesign based on coefficient reliability and improved information bitdistribution in accordance with aspects of the present disclosure. Theoperations of method 3600 may be implemented by a UE 115 or itscomponents as described herein. For example, the operations of method3600 may be performed by a UE communications manager as described withreference to FIGS. 26 through 29. In some examples, a UE 115 may executea set of codes to control the functional elements of the device toperform the functions described below. Additionally or alternatively,the UE 115 may perform aspects of the functions described below usingspecial-purpose hardware.

At 3605 the UE 115 may receive a codeword over a wireless channel, wherethe codeword is based on multiple information bits encoded using a polarcode having multiple bit channels. The operations of 3605 may beperformed according to the methods described herein. In certainexamples, aspects of the operations of 3605 may be performed by acodeword processor as described with reference to FIGS. 26 through 29.

At 3610 the UE 115 may select a bit index reliability sequence for themultiple bit channels based on a length of the codeword, where an orderof bit indices in the bit index reliability sequence is determined basedon applying a UPO to an input search sequence to obtain a partial order,applying an analytical method to obtain calculated relative orders ofbit indices not ordered in the partial order, and applying a simulationto refine an order of at least two bit indices selected based on thecalculated relative orders. The operations of 3610 may be performedaccording to the methods described herein. In certain examples, aspectsof the operations of 3610 may be performed by a sequence identifier asdescribed with reference to FIGS. 26 through 29.

At 3615 the UE 115 may decode the codeword based on the bit indexreliability sequence. The operations of 3615 may be performed accordingto the methods described herein. In certain examples, aspects of theoperations of 3615 may be performed by a decoder as described withreference to FIGS. 26 through 29.

FIG. 37 shows a flowchart illustrating a method 3700 for polar sequencedesign based on coefficient reliability and improved information bitdistribution in accordance with aspects of the present disclosure. Theoperations of method 3700 may be implemented by a base station 105 orits components as described herein. For example, the operations ofmethod 3700 may be performed by a base station communications manager asdescribed with reference to FIGS. 30 through 33. In some examples, abase station 105 may execute a set of codes to control the functionalelements of the device to perform the functions described below.Additionally or alternatively, the base station 105 may perform aspectsof the functions described below using special-purpose hardware.

At 3705 the base station 105 may determine a bit index reliabilitysequence for multiple bit channels of a polar code based on a length ofa codeword, where an order of bit indices in the reliability sequence isdetermined based on applying a UPO to an input search sequence to obtaina partial order, applying an analytical method to obtain calculatedrelative orders of bit indices not ordered in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated relative orders. The operations of 3705may be performed according to the methods described herein. In certainexamples, aspects of the operations of 3705 may be performed by asequence identifier as described with reference to FIGS. 30 through 33.

At 3710 the base station 105 may generate the codeword according to thepolar code based on the bit index reliability sequence and multipleinformation bits encoded using the polar code. The operations of 3710may be performed according to the methods described herein. In certainexamples, aspects of the operations of 3710 may be performed by acodeword processor as described with reference to FIGS. 30 through 33.

At 3715 the base station 105 may transmit the codeword. The operationsof 3715 may be performed according to the methods described herein. Incertain examples, aspects of the operations of 3715 may be performed bya codeword processor as described with reference to FIGS. 30 through 33.

It is to be understood that although the diagrams, devices, and modulesdescribed above often describe a base station 105 encoding a signal anda UE 115 decoding a signal, the roles of these devices may be reversedor interchanged. For example, a UE 115 may contain one or more of thecomponents and/or modules described above with respect to a base station105 in order to encode a codeword according to the described techniques.Similarly, a base station 105 may contain one or more of the componentsand/or modules described above with respect to a UE 115 in order todecode a received codeword.

It should be noted that the methods described above describe possibleimplementations, and that the operations and the steps may be rearrangedor otherwise modified and that other implementations are possible.Further, aspects from two or more of the methods may be combined.

Techniques described herein may be used for various wirelesscommunications systems such as code division multiple access (CDMA),time division multiple access (TDMA), frequency division multiple access(FDMA), orthogonal frequency division multiple access (OFDMA), singlecarrier frequency division multiple access (SC-FDMA), and other systems.A CDMA system may implement a radio technology such as CDMA2000,Universal Terrestrial Radio Access (UTRA), etc. CDMA2000 covers IS-2000,IS-95, and IS-856 standards. IS-2000 Releases may be commonly referredto as CDMA2000 1×, 1×, etc. IS-856 (TIA-856) is commonly referred to asCDMA2000 1×EV-DO, High Rate Packet Data (HRPD), etc. UTRA includesWideband CDMA (WCDMA) and other variants of CDMA. A TDMA system mayimplement a radio technology such as Global System for MobileCommunications (GSM).

An OFDMA system may implement a radio technology such as Ultra MobileBroadband (UMB), Evolved UTRA (E-UTRA), Institute of Electrical andElectronics Engineers (IEEE) 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE802.20, Flash-OFDM, etc. UTRA and E-UTRA are part of Universal MobileTelecommunications System (UMTS). LTE and LTE-A are releases of UMTSthat use E-UTRA. UTRA, E-UTRA, UMTS, LTE, LTE-A, NR, and GSM aredescribed in documents from the organization named “3rd GenerationPartnership Project” (3GPP). CDMA2000 and UMB are described in documentsfrom an organization named “3rd Generation Partnership Project 2”(3GPP2). The techniques described herein may be used for the systems andradio technologies mentioned above as well as other systems and radiotechnologies. While aspects of an LTE or an NR system may be describedfor purposes of example, and LTE or NR terminology may be used in muchof the description, the techniques described herein are applicablebeyond LTE or NR applications.

A macro cell generally covers a relatively large geographic area (e.g.,several kilometers in radius) and may allow unrestricted access by UEs115 with service subscriptions with the network provider. A small cellmay be associated with a lower-powered base station 105, as comparedwith a macro cell, and a small cell may operate in the same or different(e.g., licensed, unlicensed, etc.) frequency bands as macro cells. Smallcells may include pico cells, femto cells, and micro cells according tovarious examples. A pico cell, for example, may cover a small geographicarea and may allow unrestricted access by UEs 115 with servicesubscriptions with the network provider. A femto cell may also cover asmall geographic area (e.g., a home) and may provide restricted accessby UEs 115 having an association with the femto cell (e.g., UEs 115 in aclosed subscriber group (CSG), UEs 115 for users in the home, and thelike). An eNB for a macro cell may be referred to as a macro eNB. An eNBfor a small cell may be referred to as a small cell eNB, a pico eNB, afemto eNB, or a home eNB. An eNB may support one or multiple (e.g., two,three, four, and the like) cells, and may also support communicationsusing one or multiple component carriers.

The wireless communications system 100 or systems described herein maysupport synchronous or asynchronous operation. For synchronousoperation, the base stations 105 may have similar frame timing, andtransmissions from different base stations 105 may be approximatelyaligned in time. For asynchronous operation, the base stations 105 mayhave different frame timing, and transmissions from different basestations 105 may not be aligned in time. The techniques described hereinmay be used for either synchronous or asynchronous operations.

Information and signals described herein may be represented using any ofa variety of different technologies and techniques. For example, data,instructions, commands, information, signals, bits, symbols, and chipsthat may be referenced throughout the above description may berepresented by voltages, currents, electromagnetic waves, magneticfields or particles, optical fields or particles, or any combinationthereof.

The various illustrative blocks and modules described in connection withthe disclosure herein may be implemented or performed with ageneral-purpose processor, a DSP, an ASIC, an FPGA or other programmablelogic device (PLD), discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. A general-purpose processor may be a microprocessor,but in the alternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices (e.g., a combinationof a DSP and a microprocessor, multiple microprocessors, one or moremicroprocessors in conjunction with a DSP core, or any other suchconfiguration).

The functions described herein may be implemented in hardware, softwareexecuted by a processor, firmware, or any combination thereof. Ifimplemented in software executed by a processor, the functions may bestored on or transmitted over as one or more instructions or code on acomputer-readable medium. Other examples and implementations are withinthe scope of the disclosure and appended claims. For example, due to thenature of software, functions described above can be implemented usingsoftware executed by a processor, hardware, firmware, hardwiring, orcombinations of any of these. Features implementing functions may alsobe physically located at various positions, including being distributedsuch that portions of functions are implemented at different physicallocations.

Computer-readable media includes both non-transitory computer storagemedia and communication media including any medium that facilitatestransfer of a computer program from one place to another. Anon-transitory storage medium may be any available medium that can beaccessed by a general purpose or special purpose computer. By way ofexample, and not limitation, non-transitory computer-readable media mayinclude random-access memory (RAM), read-only memory (ROM), electricallyerasable programmable read only memory (EEPROM), flash memory, compactdisk (CD) ROM or other optical disk storage, magnetic disk storage orother magnetic storage devices, or any other non-transitory medium thatcan be used to carry or store desired program code means in the form ofinstructions or data structures and that can be accessed by ageneral-purpose or special-purpose computer, or a general-purpose orspecial-purpose processor. Also, any connection is properly termed acomputer-readable medium. For example, if the software is transmittedfrom a website, server, or other remote source using a coaxial cable,fiber optic cable, twisted pair, digital subscriber line (DSL), orwireless technologies such as infrared, radio, and microwave, then thecoaxial cable, fiber optic cable, twisted pair, DSL, or wirelesstechnologies such as infrared, radio, and microwave are included in thedefinition of medium. Disk and disc, as used herein, include CD, laserdisc, optical disc, digital versatile disc (DVD), floppy disk andBlu-ray disc where disks usually reproduce data magnetically, whilediscs reproduce data optically with lasers. Combinations of the aboveare also included within the scope of computer-readable media.

As used herein, including in the claims, “or” as used in a list of items(e.g., a list of items prefaced by a phrase such as “at least one of” or“one or more of”) indicates an inclusive list such that, for example, alist of at least one of A, B, or C means A or B or C or AB or AC or BCor ABC (i.e., A and B and C). Also, as used herein, the phrase “basedon” shall not be construed as a reference to a closed set of conditions.For example, an exemplary step that is described as “based on conditionA” may be based on both a condition A and a condition B withoutdeparting from the scope of the present disclosure. In other words, asused herein, the phrase “based on” shall be construed in the same manneras the phrase “based at least in part on.”

In the appended figures, similar components or features may have thesame reference label. Further, various components of the same type maybe distinguished by following the reference label by a dash and a secondlabel that distinguishes among the similar components. If just the firstreference label is used in the specification, the description isapplicable to any one of the similar components having the same firstreference label irrespective of the second reference label, or othersubsequent reference label.

The description set forth herein, in connection with the appendeddrawings, describes example configurations and does not represent allthe examples that may be implemented or that are within the scope of theclaims. The term “exemplary” used herein means “serving as an example,instance, or illustration,” and not “preferred” or “advantageous overother examples.” The detailed description includes specific details forthe purpose of providing an understanding of the described techniques.These techniques, however, may be practiced without these specificdetails. In some instances, well-known structures and devices are shownin block diagram form in order to avoid obscuring the concepts of thedescribed examples.

The description herein is provided to enable a person skilled in the artto make or use the disclosure. Various modifications to the disclosurewill be readily apparent to those skilled in the art, and the genericprinciples defined herein may be applied to other variations withoutdeparting from the scope of the disclosure. Thus, the disclosure is notlimited to the examples and designs described herein, but is to beaccorded the broadest scope consistent with the principles and novelfeatures disclosed herein.

What is claimed is:
 1. A method for wireless communication, comprising:receiving a codeword over a wireless channel, wherein the codeword isbased on a plurality of information bits encoded using a polar codehaving a plurality of bit channels; selecting a bit index reliabilitysequence for the plurality of bit channels based on a length of thecodeword, wherein an order of bit indices in the bit index reliabilitysequence is determined based on applying a universal partial order (UPO)to an input search sequence to obtain a partial order, applying ananalytical method to obtain calculated orders of bit indices that areunordered relative to one another in the partial order, and applying asimulation to refine an order of at least two bit indices selected basedon the calculated orders; and decoding the codeword based on the bitindex reliability sequence.
 2. The method of claim 1, wherein decodingthe codeword comprises: applying a successive cancellation list decodingalgorithm to a signal that comprises the codeword.
 3. The method ofclaim 2, wherein the simulation is based on a list size applied by thesuccessive cancellation list decoding algorithm.
 4. The method of claim1, wherein the simulation is a link-level performance simulation.
 5. Themethod of claim 1, wherein the length of the codeword is 128 bits, andthe bit index reliability sequence is: [127, 126, 125, 123, 119, 111,124, 95, 122, 121, 118, 63, 117, 110, 115, 109, 94, 107, 93, 62, 103,120, 91, 116, 61, 87, 114, 59, 108, 79, 113, 55, 106, 92, 47, 105, 102,31, 90, 101, 89, 60, 86, 99, 58, 85, 78, 112, 57, 54, 83, 77, 104, 53,46, 75, 100, 51, 45, 71, 88, 30, 98, 43, 84, 29, 97, 39, 27, 56, 82, 76,23, 52, 15, 81, 74, 44, 50, 73, 70, 42, 49, 69, 28, 96, 41, 67, 38, 26,37, 25, 22, 80, 35, 21, 72, 14, 48, 19, 13, 68, 40, 11, 7, 66, 36, 24,65, 34, 20, 33, 18, 12, 17, 10, 9, 6, 64, 5, 3, 32, 16, 8, 4, 2, 1, 0].6. The method of claim 1, wherein the length of the codeword is 256bits, and the bit index reliability sequence is: [255, 254, 253, 251,247, 239, 252, 223, 250, 249, 246, 191, 245, 238, 243, 237, 127, 222,235, 221, 248, 190, 231, 219, 244, 189, 215, 242, 126, 187, 236, 207,241, 125, 234, 183, 220, 233, 123, 230, 175, 218, 229, 119, 159, 214,217, 111, 188, 227, 186, 213, 95, 206, 240, 185, 211, 182, 124, 205,203, 232, 181, 63, 174, 122, 228, 179, 199, 121, 173, 216, 158, 118,226, 117, 171, 212, 110, 157, 225, 115, 167, 184, 204, 109, 155, 210,94, 180, 107, 151, 209, 202, 93, 143, 178, 62, 172, 103, 201, 61, 198,120, 177, 91, 170, 197, 87, 116, 156, 195, 114, 169, 79, 59, 166, 224,108, 154, 113, 165, 55, 153, 106, 208, 150, 92, 163, 47, 102, 149, 200,105, 90, 142, 31, 101, 176, 147, 89, 141, 196, 86, 60, 99, 139, 168, 85,58, 194, 78, 135, 57, 164, 83, 112, 54, 77, 152, 193, 46, 53, 162, 104,75, 148, 51, 100, 71, 45, 161, 30, 146, 140, 88, 43, 98, 29, 145, 138,84, 39, 97, 27, 137, 82, 56, 76, 23, 134, 192, 133, 52, 15, 81, 74, 50,44, 131, 73, 70, 160, 42, 49, 69, 28, 144, 41, 67, 26, 38, 96, 136, 37,25, 22, 132, 35, 80, 21, 14, 72, 130, 19, 13, 48, 68, 11, 129, 40, 7,66, 36, 24, 65, 34, 20, 33, 18, 12, 17, 10, 128, 6, 9, 5, 64, 3, 32, 16,8, 4, 2, 1, 0].
 7. The method of claim 1, wherein the length of thecodeword is 512 bits, and at least a portion of the bit indexreliability sequence is: [511, 510, 509, 507, 503, 495, 508, 479, 506,505, 502, 447, 501, 494, 499, 493, 383, 478, 491, 477, 504, 487, 475,446, 500, 255, 445, 471, 498, 492, 443, 497, 382, 463, 490, 439, 381,476, 489, 486, 379, 474, 431, 485, 473, 254, 444, 375, 470, 483, 253,415, 442, 469, 496, 367, 462, 251, 441, 467, 438, 380, 461, 247, 351,488, 430, 459, 239, 437, 378, 319, 435, 484, 223, 429, 455, 377, 472,374, 414, 482, 252, 427, 373, 191, 468, 366, 413, 466, 423, 250, 481,371, 440, 365, 411, 460, 249, 350, 246, 436, 407, 349, 458, 465, 363,238, 399, 127, 434, 428, 245, 359, 454, 318, 457, 376, 347, 243, 433,237, 426, 453, 222, 343, 372, 412, 317, 235, 425, 451, 370, 315, 422,221, 480, 364, 335, 410, 231, 190, 369, 421, 311, 409, 219, 248, 464,362, 406, 348, 419, 189, 244, 303, 358, 215, 405, 456, 361, 398, 126,242, 346, 187, 236, 403, 357, 316, 432, 207, 287, 397, 452, 342, 125,345, 234, 241, 123, 355, 395, 424, 183, 314, 341, 220, 450, 233, 391,334, 230, 420, 175, 313, 218, 119, 339, 368, 310, 408, 229, 333, 449,214, 159, 217, 309, 360, 331, 418, 188, 227, 302, 404, 111, 213, 307].8. The method of claim 1, wherein the analytical method comprises anindex polarization weight rule, or a Reed-Muller rule, or a densityevolution (DE) rule, or a mutual information-DE (MI-DE) rule, or anycombination thereof.
 9. The method of claim 1, wherein the order of bitindices in the bit index reliability sequence is further determinedbased on selecting a bit index from the input search sequence based onthe partial order, the method further comprising: adding the selectedbit index to the bit index reliability sequence.
 10. The method of claim9, further comprising: removing the selected bit index from the inputsearch sequence to generate an input search subsequence; calculating asecond partial order under the UPO of the input search subsequence; andselecting a bit index from the input search subsequence based on thesecond partial order.
 11. The method of claim 1, wherein the UPOcomprises a first property and a second property, and wherein thecalculated orders of bit indices violate at least one of the firstproperty or the second property.
 12. The method of claim 1, furthercomprising: modifying a portion of the bit index reliability sequenceusing a second sequence to generate a modified bit index reliabilitysequence, wherein decoding the codeword comprises: decoding the codewordbased on the modified bit index reliability sequence.
 13. A method forwireless communication, comprising: determining a bit index reliabilitysequence for a plurality of bit channels of a polar code based on alength of a codeword, wherein an order of bit indices in the bit indexreliability sequence is determined based on applying a universal partialorder (UPO) to an input search sequence to obtain a partial order,applying an analytical method to obtain calculated orders of bit indicesthat are unordered relative to one another in the partial order, andapplying a simulation to refine an order of at least two bit indicesselected based on the calculated orders; generating the codewordaccording to the polar code based on the bit index reliability sequenceand a plurality of information bits encoded using the polar code; andtransmitting the codeword.
 14. The method of claim 13, wherein thesimulation is a link-level performance simulation.
 15. The method ofclaim 13, wherein the length of the codeword is 128 bits, and the bitindex reliability sequence is: [127, 126, 125, 123, 119, 111, 124, 95,122, 121, 118, 63, 117, 110, 115, 109, 94, 107, 93, 62, 103, 120, 91,116, 61, 87, 114, 59, 108, 79, 113, 55, 106, 92, 47, 105, 102, 31, 90,101, 89, 60, 86, 99, 58, 85, 78, 112, 57, 54, 83, 77, 104, 53, 46, 75,100, 51, 45, 71, 88, 30, 98, 43, 84, 29, 97, 39, 27, 56, 82, 76, 23, 52,15, 81, 74, 44, 50, 73, 70, 42, 49, 69, 28, 96, 41, 67, 38, 26, 37, 25,22, 80, 35, 21, 72, 14, 48, 19, 13, 68, 40, 11, 7, 66, 36, 24, 65, 34,20, 33, 18, 12, 17, 10, 9, 6, 64, 5, 3, 32, 16, 8, 4, 2, 1, 0].
 16. Themethod of claim 13, wherein the length of the codeword is 256 bits, andthe bit index reliability sequence is: [255, 254, 253, 251, 247, 239,252, 223, 250, 249, 246, 191, 245, 238, 243, 237, 127, 222, 235, 221,248, 190, 231, 219, 244, 189, 215, 242, 126, 187, 236, 207, 241, 125,234, 183, 220, 233, 123, 230, 175, 218, 229, 119, 159, 214, 217, 111,188, 227, 186, 213, 95, 206, 240, 185, 211, 182, 124, 205, 203, 232,181, 63, 174, 122, 228, 179, 199, 121, 173, 216, 158, 118, 226, 117,171, 212, 110, 157, 225, 115, 167, 184, 204, 109, 155, 210, 94, 180,107, 151, 209, 202, 93, 143, 178, 62, 172, 103, 201, 61, 198, 120, 177,91, 170, 197, 87, 116, 156, 195, 114, 169, 79, 59, 166, 224, 108, 154,113, 165, 55, 153, 106, 208, 150, 92, 163, 47, 102, 149, 200, 105, 90,142, 31, 101, 176, 147, 89, 141, 196, 86, 60, 99, 139, 168, 85, 58, 194,78, 135, 57, 164, 83, 112, 54, 77, 152, 193, 46, 53, 162, 104, 75, 148,51, 100, 71, 45, 161, 30, 146, 140, 88, 43, 98, 29, 145, 138, 84, 39,97, 27, 137, 82, 56, 76, 23, 134, 192, 133, 52, 15, 81, 74, 50, 44, 131,73, 70, 160, 42, 49, 69, 28, 144, 41, 67, 26, 38, 96, 136, 37, 25, 22,132, 35, 80, 21, 14, 72, 130, 19, 13, 48, 68, 11, 129, 40, 7, 66, 36,24, 65, 34, 20, 33, 18, 12, 17, 10, 128, 6, 9, 5, 64, 3, 32, 16, 8, 4,2, 1, 0].
 17. The method of claim 13, wherein the length of the codewordis 512 bits, and a portion of the bit index reliability sequence is:[511, 510, 509, 507, 503, 495, 508, 479, 506, 505, 502, 447, 501, 494,499, 493, 383, 478, 491, 477, 504, 487, 475, 446, 500, 255, 445, 471,498, 492, 443, 497, 382, 463, 490, 439, 381, 476, 489, 486, 379, 474,431, 485, 473, 254, 444, 375, 470, 483, 253, 415, 442, 469, 496, 367,462, 251, 441, 467, 438, 380, 461, 247, 351, 488, 430, 459, 239, 437,378, 319, 435, 484, 223, 429, 455, 377, 472, 374, 414, 482, 252, 427,373, 191, 468, 366, 413, 466, 423, 250, 481, 371, 440, 365, 411, 460,249, 350, 246, 436, 407, 349, 458, 465, 363, 238, 399, 127, 434, 428,245, 359, 454, 318, 457, 376, 347, 243, 433, 237, 426, 453, 222, 343,372, 412, 317, 235, 425, 451, 370, 315, 422, 221, 480, 364, 335, 410,231, 190, 369, 421, 311, 409, 219, 248, 464, 362, 406, 348, 419, 189,244, 303, 358, 215, 405, 456, 361, 398, 126, 242, 346, 187, 236, 403,357, 316, 432, 207, 287, 397, 452, 342, 125, 345, 234, 241, 123, 355,395, 424, 183, 314, 341, 220, 450, 233, 391, 334, 230, 420, 175, 313,218, 119, 339, 368, 310, 408, 229, 333, 449, 214, 159, 217, 309, 360,331, 418, 188, 227, 302, 404, 111, 213, 307].
 18. The method of claim13, wherein the analytical method comprises an index polarization weightrule, or a Reed-Muller rule, or a density evolution (DE) rule, or amutual information-DE (MI-DE) rule, or any combination thereof.
 19. Themethod of claim 13, wherein the order of bit indices in the bit indexreliability sequence is further determined based on selecting a bitindex from the input search sequence based on the partial order, themethod further comprising: adding the selected bit index to the bitindex reliability sequence.
 20. The method of claim 19, furthercomprising: removing the selected bit index from the input searchsequence to generate an input search subsequence; calculating a secondpartial order under the UPO of the input search subsequence; andselecting a bit index from the input search subsequence based on thesecond partial order.
 21. The method of claim 13, wherein the UPOcomprises a first property and a second property, and wherein thecalculated orders of bit indices violate at least one of the firstproperty or the second property.
 22. The method of claim 13, furthercomprising: modifying a portion of the bit index reliability sequenceusing a second sequence to generate a modified bit index reliabilitysequence, wherein generating the codeword comprises: generating thecodeword based on the modified bit index reliability sequence.
 23. Amethod for wireless communication, comprising: identifying a pluralityof information bits for encoding using a polar code having a pluralityof bit channels; identifying a set of bit locations of the plurality ofbit channels of the polar code for the plurality of information bitsbased on a bit index reliability sequence, wherein the bit indexreliability sequence is determined based on a binary bit weighting forthe plurality of bit channels that applies a plurality of weightingfactors; generating a codeword according to the polar code based on thebit index reliability sequence and the plurality of information bits;and transmitting the codeword.
 24. The method of claim 23, wherein thebit index reliability sequence is determined based on performing thebinary bit weighting using a first weighting factor to obtain a firstreliability sequence for the plurality of bit channels, the methodfurther comprising: modifying a subset of the first reliability sequenceby performing the binary bit weighting using a second weighting factorto obtain a second reliability sequence for the subset of the firstreliability sequence.
 25. The method of claim 24, wherein the bit indexreliability sequence is determined based on: modifying a subset of thesecond reliability sequence by performing the binary bit weighting usinga third weighting factor to obtain a third reliability sequence for thesubset of the second reliability sequence.
 26. The method of claim 24,wherein the subset of the first reliability sequence comprises aplurality of bit channels having lowest bit channel indices in the firstreliability sequence.
 27. The method of claim 24, wherein the subset ofthe first reliability sequence comprises a plurality of bit channelshaving highest bit channel indices in the first reliability sequence.28. The method of claim 23, wherein the bit index reliability sequenceis determined based on: performing the binary bit weighting using afirst weighting factor for a first subset of bit indices and a secondweighting factor for a second subset of bit indices.
 29. The method ofclaim 28, wherein the bit index reliability sequence is determined basedon: performing the binary bit weighting using a third weighting factorfor a third subset of bit indices.
 30. A memory of an apparatus,instructions stored in the memory and operable, when executed by aprocessor of the apparatus, to cause the apparatus to receive, over awireless channel, a codeword that is based on a plurality of informationbits encoded using a polar code having a plurality of bit channels,select a bit index reliability sequence for the plurality of bitchannels based on a length of the codeword, and decode the codewordbased on the bit index reliability sequence, wherein an order of bitindices in the bit index reliability sequence is determined by a processcomprising: applying a universal partial order (UPO) to an input searchsequence to obtain a partial order; applying an analytical method toobtain calculated orders of bit indices that are unordered relative toone another in the partial order; and applying a simulation to refine anorder of at least two bit indices selected based on the calculatedorders.